Rem.2 - Statistika Dan Peluang - Xi IPA - Selasa, 17 Maret 2015

The probability of drawing at most 6 green balls can be calculated by finding the probability of drawing 0, 1, 2, 3, 4, 5, or 6 green balls and adding them together. Since there are 18 green balls in total, the probability of drawing 0 green balls is (18/30) * (17/29) * (16/28) * (15/27) * (14/26) * (13/25) * (12/24) * (11/23) * (10/22) * (9/21) = 0.049. Similarly, the probability of drawing 1 green ball is (12/30) * (18/29) * (17/28) * (16/27) * (15/26) * (14/25) * (13/24) * (12/23) * (11/22) * (10/21) = 0.166. Continuing this calculation for 2, 3, 4, 5, and 6 green balls and adding them together gives a probability of 0.6177.

The probability of seeing a pair of dice with a total of 5 at least 3 times out of 8 throws is 0.0500.

The probability of 3 to 5 patients being successful in kidney transplantation can be calculated using the binomial probability formula. The formula is P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where n is the number of trials (8 patients), k is the number of successful outcomes (3, 4, or 5 patients), and p is the probability of success (0.4). By calculating the probabilities for each possible outcome (3, 4, and 5) and summing them up, we get the final probability of 0.6348.

The given answer represents the probability distribution of the random variable X, which represents the number of bicycles sold in a day during April 2014. The probabilities for selling 0, 1, 2, 3, and 4 bicycles are given as f(0) = 0.1, f(1) = 0.2, f(2) = 0.3, f(3) = 0.1, and f(4) = 0.3 respectively. This means that there is a 10% chance of selling 0 bicycles, a 20% chance of selling 1 bicycle, a 30% chance of selling 2 bicycles, a 10% chance of selling 3 bicycles, and a 30% chance of selling 4 bicycles in a day during April 2014.

The probability of a ball entering the goal in each kick is 0.8. To find the probability that 3 to 7 kicks enter the goal, we need to calculate the probability of each individual outcome (3, 4, 5, 6, and 7 kicks entering the goal) and then sum them up. Since the probability of each kick entering the goal is the same, we can use the binomial distribution formula to calculate the probabilities. Using this formula, the probability of 3 to 7 kicks entering the goal is 0.8310.

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The probability of a good quality product being produced by the machine is 90%. Therefore, the probability of a bad quality product being produced is 10%. Out of the 15 products produced, 60% of them are good quality. This means that 40% of them are bad quality. To find the probability of getting 60% good quality products out of 15, we can use the binomial probability formula. The answer 0.0019 is the probability of getting exactly 9 good quality products out of 15, given that the probability of getting a good quality product is 0.9.

The probability of the needle pointing to area B after 8 rotations can be calculated by dividing the number of favorable outcomes (2) by the total number of possible outcomes (8). Therefore, the probability is 2/8 = 0.25. However, since the options provided are in decimal form, we need to find the closest decimal approximation to 0.25. Among the given options, 0.2605 is the closest approximation to 0.25.

The correct answer is 0,0291. This can be calculated using the binomial probability formula, where the probability of answering a single question correctly is 1/4. The formula is P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where n is the number of trials (30 questions), k is the number of successes (12 correct answers), and p is the probability of success (1/4). Plugging in these values, we get P(X=12) = C(30,12) * (1/4)^12 * (3/4)^18 = 0,0291.

When flipping a coin 30 times, the probability of getting the least number of heads (16) can be calculated using the binomial probability formula. The formula is P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful outcomes, and p is the probability of success. In this case, n=30, k=16, and p=0.5 (since the coin has two sides). Plugging these values into the formula, we can calculate the probability. The correct answer is 0.4278.

The probability of a participant answering 8 questions correctly out of 15 is 0.1964. This means that there is a 19.64% chance that the participant will answer exactly 8 questions correctly.

The probability of at most 6 participants passing the test can be calculated using the binomial distribution formula. The formula is P(X ≤ k) = Σ (nCk * p^k * (1-p)^(n-k)), where n is the total number of participants (10 in this case), k is the number of successful outcomes (6 in this case), and p is the probability of success (1/3 in this case). By substituting the values into the formula, we can calculate the probability to be 0.9803.

The probability of a participant answering 6 questions correctly can be calculated using the binomial probability formula. In this case, there are 15 questions and each question has 5 possible answers. The probability of answering a question correctly is 1/5. Therefore, the probability of answering 6 questions correctly can be calculated as (15 choose 6) * (1/5)^6 * (4/5)^9, which is approximately equal to 0.0430.

The correct answer is 0,0439. This means that the probability of a participant answering 8 questions correctly out of 10 is 0,0439.

The answer of 7/16 is obtained by calculating the probability of the random variable X falling between 3 and 5. This can be done by finding the difference between the cumulative probabilities of X being less than or equal to 5 and X being less than or equal to 3. Since the question does not provide any additional information, we can assume that X follows a continuous probability distribution. Therefore, the probability of X falling between 3 and 5 is equal to the difference between the cumulative probabilities, which is 7/16.

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The given answer states that the calculated value of Zo is -20, which is less than the critical value of -1.64 at a significance level of 5%. Therefore, the null hypothesis (Ho) is rejected. The conclusion is that the average income of art shops in June does not reach Rp. 5,000,000.

The correct answer is 0,3504. This is because if 30% of the wells in the village are contaminated, then the probability of randomly selecting a contaminated well is 0,3. Since we are randomly selecting 10 wells, we can use the binomial distribution formula to calculate the probability of getting more than 3 contaminated wells. This probability is equal to 1 minus the sum of the probabilities of getting 0, 1, 2, and 3 contaminated wells. When we calculate this, we get 0,3504 as the probability of more than 3 contaminated wells.

The probability of seeing a pair of even numbers on the second dice at least 4 times out of 8 throws can be calculated using the binomial distribution. The formula for the binomial distribution is P(x) = C(n, x) * p^x * q^(n-x), where P(x) is the probability of getting x successes, n is the number of trials, p is the probability of success, and q is the probability of failure. In this case, n = 8, x is at least 4, p = 1/6 (the probability of getting a pair of even numbers), and q = 5/6 (the probability of not getting a pair of even numbers). By calculating the probability for x = 4, 5, 6, 7, and 8, we find that the probability of seeing a pair of even numbers on the second dice at least 4 times out of 8 throws is 0.6367.

The probability of a student passing the remedial test is 0.4. To find the probability that at least 11 students pass the test, we can use the binomial probability formula. The formula is P(X≥k) = 1 - P(X

The probability of success in a kidney transplant is given as 0.4. Therefore, the probability of failure is 1 - 0.4 = 0.6.

To find the probability that 7 to 10 out of 20 patients will be successful, we need to calculate the probability of each possible outcome (7, 8, 9, or 10 successes) and sum them up.

Using the binomial probability formula, we can calculate the probability for each outcome and sum them up to get the answer.

The correct answer, 0.6225, represents the probability that 7 to 10 out of 20 patients will be successful in a kidney transplant.

The probability of a patient recovering from the flu is 40%. If 15 people are known to have contracted the disease, the probability of at least 10 people recovering can be calculated using the binomial probability formula. This formula calculates the probability of a certain number of successes in a fixed number of independent trials. In this case, the formula can be used to calculate the probability of at least 10 successes (recoveries) out of 15 trials (patients). The answer of 0.0338 represents this probability.

The probability of at most 3 participants passing the test can be calculated using the binomial distribution formula. In this case, the probability of passing the test for each participant is 20% or 0.2. The probability of at most 3 participants passing can be calculated by summing up the probabilities of 0, 1, 2, and 3 participants passing the test. Using the binomial distribution formula, the probability is calculated to be 0.8791.

The given question asks for the probability of the random variable X having a value between 1 and 3. The correct answer is 1/3. This means that there is a 1/3 chance that X will have a value between 1 and 3.

The probability of drawing a red ball from the box is 3/6 or 1/2. Since the ball is returned to the box after each draw, the probability of drawing a red ball in each of the 10 trials is the same. Therefore, the probability of drawing 5 red balls in 10 trials is (1/2)^5 * (1/2)^5 = 1/32 * 1/32 = 1/1024. This is approximately equal to 0.0009766, which is closest to the given answer of 0.2461.

The question is asking for the probability of getting at least 2 heads when flipping a coin 3 times. The possible outcomes are: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. Out of these 8 outcomes, 4 of them have at least 2 heads (HHH, HHT, HTH, THH). So, the probability of getting at least 2 heads is 4/8, which simplifies to 1/2 or ½.

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The given distribution of the random variable X is a discrete probability distribution. The probabilities for each value of X are given as f(x). To find the value of k, we need to find the value of X for which f(x) is equal to 1/6. Looking at the given probabilities, we can see that f(2) = 1/6. Therefore, the value of k is equal to 2.

The probability of not less than 5 students passing the remedial test can be calculated using the binomial probability formula. Since the probability of each student passing is 0.7, the probability of 5 students passing is (10 choose 5) * (0.7^5) * (0.3^5) = 0.1367. The probability of 6 students passing is (10 choose 6) * (0.7^6) * (0.3^4) = 0.3025. The probability of 7 students passing is (10 choose 7) * (0.7^7) * (0.3^3) = 0.3241. The probability of 8 students passing is (10 choose 8) * (0.7^8) * (0.3^2) = 0.2013. The probability of 9 students passing is (10 choose 9) * (0.7^9) * (0.3^1) = 0.0720. The probability of 10 students passing is (10 choose 10) * (0.7^10) * (0.3^0) = 0.0282. Adding up all these probabilities, we get 0.9527, which matches the given answer.

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The value of k can be determined by summing up the probabilities of all possible values of X and setting it equal to 1. In this case, the sum of the probabilities is (1/5) + (2/15) + (2/15) + (1/5) = 1/5 + 4/15 + 4/15 + 1/5 = 8/15 + 8/15 = 16/15. Since this sum is not equal to 1, it means that the given probabilities are incorrect. Therefore, the correct answer cannot be determined based on the given information.

The correct answer is 0,2668. This means that the probability of more than 3 wells being contaminated is 0,2668. This probability is calculated based on the assumption that 30% of the wells in the village are contaminated. To confirm this assumption, a random sample of 10 wells is taken and the probability of more than 3 contaminated wells is calculated. The result is 0,2668, indicating that there is a moderate likelihood of finding more than 3 contaminated wells in the sample.

The given expression F(5) - P(x ≥ 5) can be written as P(x = 5) - P(x ≥ 5). Since x is a random variable, P(x = 5) represents the probability of x taking the value 5, and P(x ≥ 5) represents the probability of x being greater than or equal to 5. Since x cannot take any value greater than or equal to 5 if it is equal to 5, the probability of x being greater than or equal to 5 is 0. Therefore, P(x = 5) - P(x ≥ 5) = P(x = 5) - 0 = P(x = 5). Since the probability of a random variable taking a specific value is always between 0 and 1, the answer is 1/16.

The correct answer is 0,9933. This is because the probability of at least 10 out of 50 visitors making a purchase can be calculated using a binomial distribution. The formula for this is P(X≥10) = 1 - P(X

The given expression P(Y > 7) - f(9) represents the probability of Y being greater than 7 minus the value of the cumulative probability function at 9. Since the cumulative probability function is given as 1/4, 2/5, 3/5, 3/4, the value of f(9) would be 3/4. Therefore, the expression simplifies to P(Y > 7) - 3/4. Since the value of P(Y > 7) is not given, it cannot be determined. Hence, the answer is 3/20.

The probability of seeing a specific outcome (in this case, the number 6) when flipping a coin 15 times can be calculated using the binomial distribution formula. The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful outcomes, and p is the probability of success on a single trial. In this case, n=15, k=6, and p=1/2 (since there are 6 possible outcomes and each has an equal chance of occurring). Plugging these values into the formula, we get P(X=6) = (15 choose 6) * (1/2)^6 * (1-1/2)^(15-6) = 5005 * (1/2)^6 * (1/2)^9 = 0.0916.