X Standard (Chapter - Probability)

1) A bag contains 5 red balls and some blue balls .If the probability of drawing a blue ball is double that of a red ball, then the number of blue balls in a bag is:

5

10

15

20

Let's assume the number of blue balls in the bag is x. The probability of drawing a blue ball is x/(x+5), and the probability of drawing a red ball is 5/(x+5). According to the given information, the probability of drawing a blue ball is double that of drawing a red ball. So, we can write the equation: x/(x+5) = 2 * 5/(x+5). Solving this equation, we get x = 10. Therefore, the number of blue balls in the bag is 10.

Explanation

Let's assume the number of blue balls in the bag is x. The probability of drawing a blue ball is x/(x+5), and the probability of drawing a red ball is 5/(x+5). According to the given information, the probability of drawing a blue ball is double that of drawing a red ball. So, we can write the equation: x/(x+5) = 2 * 5/(x+5). Solving this equation, we get x = 10. Therefore, the number of blue balls in the bag is 10.

2) A fish tank has 5 male fish and 8 female fish. The probability of fish taken out is a male fish:

5/8

8/13

5/13

8/5

The probability of selecting a male fish from the tank can be determined by dividing the number of male fish (5) by the total number of fish (5 + 8 = 13). Therefore, the probability of selecting a male fish is 5/13.

Explanation

The probability of selecting a male fish from the tank can be determined by dividing the number of male fish (5) by the total number of fish (5 + 8 = 13). Therefore, the probability of selecting a male fish is 5/13.

3) If we throw two coins in air, then the probability of getting both tails will be:

1/2

1/4

2

4

When throwing two coins in the air, there are four possible outcomes: both coins can land as heads, both as tails, one as heads and one as tails, or one as tails and one as heads. Since the probability of getting tails on a single coin toss is 1/2, the probability of getting tails on both coins is 1/2 multiplied by 1/2, which equals 1/4. Therefore, the correct answer is 1/4.

Explanation

When throwing two coins in the air, there are four possible outcomes: both coins can land as heads, both as tails, one as heads and one as tails, or one as tails and one as heads. Since the probability of getting tails on a single coin toss is 1/2, the probability of getting tails on both coins is 1/2 multiplied by 1/2, which equals 1/4. Therefore, the correct answer is 1/4.

4) The probability that cannot exist among the following:

2/3

15%

-1.5

0.7

The probability of an event occurring is always between 0 and 1, inclusive. Negative numbers like -1.5 cannot represent probabilities as they are outside this range. Therefore, -1.5 cannot exist as a probability.

Explanation

The probability of an event occurring is always between 0 and 1, inclusive. Negative numbers like -1.5 cannot represent probabilities as they are outside this range. Therefore, -1.5 cannot exist as a probability.

5) A bag has 3 red balls and 5 green balls. If we take a ball from the bag, then what is the probability of getting red balls only?

1

3/8

5/8

0

The probability of getting a red ball only can be calculated by dividing the number of red balls (3) by the total number of balls in the bag (8). Therefore, the probability is 3/8.

Explanation

The probability of getting a red ball only can be calculated by dividing the number of red balls (3) by the total number of balls in the bag (8). Therefore, the probability is 3/8.

6) A card is drawn from a well shuffled deck of 52 cards. Find the probability of getting a king of red suit.

1/26

3/26

1/52

1/13

There are a total of 52 cards in a deck, and 2 of them are kings of red suits (hearts and diamonds). Therefore, the probability of drawing a king of red suit is 2/52, which simplifies to 1/26.

Explanation

There are a total of 52 cards in a deck, and 2 of them are kings of red suits (hearts and diamonds). Therefore, the probability of drawing a king of red suit is 2/52, which simplifies to 1/26.

7) A bag has 5 white marbles, 8 red marbles and 4 purple marbles. If we take a marble randomly then what is the probability of not getting purple marble?

0.6

0.33

0.08

0.77

The probability of not getting a purple marble can be calculated by dividing the number of marbles that are not purple (13) by the total number of marbles (17). Therefore, the probability is 13/17, which is approximately 0.77.

Explanation

The probability of not getting a purple marble can be calculated by dividing the number of marbles that are not purple (13) by the total number of marbles (17). Therefore, the probability is 13/17, which is approximately 0.77.

8) Two dice are thrown simultaneously. The probability of getting a sum of 9 is:

1/10

3/10

1/9

4/9

When two dice are thrown simultaneously, there are a total of 36 possible outcomes (6 outcomes for the first dice multiplied by 6 outcomes for the second dice). To find the probability of getting a sum of 9, we need to determine the number of favorable outcomes. There are 4 favorable outcomes: (3, 6), (4, 5), (5, 4), and (6, 3). Therefore, the probability of getting a sum of 9 is 4/36, which simplifies to 1/9.

Explanation

When two dice are thrown simultaneously, there are a total of 36 possible outcomes (6 outcomes for the first dice multiplied by 6 outcomes for the second dice). To find the probability of getting a sum of 9, we need to determine the number of favorable outcomes. There are 4 favorable outcomes: (3, 6), (4, 5), (5, 4), and (6, 3). Therefore, the probability of getting a sum of 9 is 4/36, which simplifies to 1/9.

9) A box of 600 bulbs contains 12 defective bulbs. One bulb is taken out at random from this box. Then the probability that it is non-defective bulb is:

143/150

147/150

1/25

1/50

Out of the 600 bulbs, 12 are defective and the remaining 588 are non-defective. When one bulb is randomly taken out, there are 588 possibilities of getting a non-defective bulb out of a total of 600 possibilities. Therefore, the probability of selecting a non-defective bulb is 588/600, which simplifies to 147/150.

Explanation

Out of the 600 bulbs, 12 are defective and the remaining 588 are non-defective. When one bulb is randomly taken out, there are 588 possibilities of getting a non-defective bulb out of a total of 600 possibilities. Therefore, the probability of selecting a non-defective bulb is 588/600, which simplifies to 147/150.

10) A card is drawn from the set of 52 cards. Find the probability of getting queen card.

1/26

1/13

4/13

5/52

There are 4 queen cards in a standard deck of 52 cards. Therefore, the probability of drawing a queen card is 4/52, which simplifies to 1/13.

Explanation

There are 4 queen cards in a standard deck of 52 cards. Therefore, the probability of drawing a queen card is 4/52, which simplifies to 1/13.

11) A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number 1,2,3……12 ,then the probability that it will point to an odd number is:

1/12

1/6

5/12

7/12

When spinning the arrow, there are a total of 12 possible outcomes since there are 12 numbers it could point to. Out of these 12 numbers, 6 of them are odd numbers (1, 3, 5, 7, 9, 11). Therefore, the probability of the arrow pointing to an odd number is 6/12, which simplifies to 1/2. This means that the correct answer is 1/6.

Explanation

When spinning the arrow, there are a total of 12 possible outcomes since there are 12 numbers it could point to. Out of these 12 numbers, 6 of them are odd numbers (1, 3, 5, 7, 9, 11). Therefore, the probability of the arrow pointing to an odd number is 6/12, which simplifies to 1/2. This means that the correct answer is 1/6.

12) The sum of the probability of an event and non event is :

2

1

0

None of these

The sum of the probability of an event and its complement (non-event) is always equal to 1. This is because the probability of either the event occurring or not occurring must be certain, or in other words, the total probability of all possible outcomes must equal 1. Therefore, the correct answer is 1.

Explanation

The sum of the probability of an event and its complement (non-event) is always equal to 1. This is because the probability of either the event occurring or not occurring must be certain, or in other words, the total probability of all possible outcomes must equal 1. Therefore, the correct answer is 1.

13) A number x is chosen at random from the numbers -2, -1, 0 , 1, 2. Then the probability that x²< 2 is?

1/5

2/5

3/5

4/5

The probability that x^2

Explanation

The probability that x^2

14) Cards marked with numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from this box randomly, then the probability that the number on card is a perfect square.

9/100

3/10

1/10

19/100

Explanation

15) What is the probability of getting 53 Mondays in a leap year?

1/7

53/366

53/365

2/7

In a leap year, there are 366 days. Since there are 7 days in a week, the probability of any specific day falling on a particular day of the week is 1/7. Therefore, the probability of getting 53 Mondays in a leap year would be 53/366, as there are 53 Mondays out of the total 366 days.

Explanation

In a leap year, there are 366 days. Since there are 7 days in a week, the probability of any specific day falling on a particular day of the week is 1/7. Therefore, the probability of getting 53 Mondays in a leap year would be 53/366, as there are 53 Mondays out of the total 366 days.