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Students will test there knowledge of probability with this short online quiz.
Questions and Answers
1.
You flip a coin twice. What is P(heads, heads)?
A.
1/2
B.
1/4
C.
3/7
D.
2/1
Correct Answer B. 1/4
Explanation When flipping a coin twice, there are four possible outcomes: heads-heads, heads-tails, tails-heads, and tails-tails. Each outcome has an equal probability of 1/4. Therefore, the probability of getting heads twice in a row is 1/4.
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2.
In a bag of colored marbles, there are 5 red, 4 blue, and 6 green marbles. If you randomly pick one marble from the bag, what is the probability that it is not blue?
A.
1/3
B.
2/3
C.
7/15
D.
11/15
Correct Answer D. 11/15
Explanation The total number of marbles is 5 red + 4 blue + 6 green = 15 marbles. The probability of not picking a blue marble includes the chances of picking either a red or a green marble, which together account for 5 red + 6 green = 11 marbles. So, the probability of not picking a blue marble is 11 out of 15, or 11/15.
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3.
You pick a marble at random. When you put the first marble back, you select a second marble at random. What is P(green, orange)?
A.
1/11
B.
2/3
C.
1/12
D.
1/18
Correct Answer D. 1/18
Explanation The probability of picking a green marble on the first draw is 1/3, as there is one green marble out of a total of three marbles. After putting the first marble back, the probability of picking an orange marble on the second draw is 4/12, as there are four orange marbles out of a total of twelve marbles remaining. Therefore, the probability of picking a green marble on the first draw and an orange marble on the second draw is (1/3) * (4/12) = 1/9. However, since we are asked for the probability of picking a green marble on the first draw and an orange marble on the second draw, we need to multiply this probability by 1/2, as the order of the marbles does not matter. Hence, the final probability is (1/9) * (1/2) = 1/18.
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4.
You spend a spinner thrice. What is the probability of P(5, even number, and 1)
A.
1/9
B.
8/864
C.
5/36
D.
1/108
Correct Answer D. 1/108
Explanation The probability of P(5, even number, and 1) can be calculated by multiplying the individual probabilities of each event occurring. The probability of rolling a 5 on the spinner is 1/6, the probability of rolling an even number is 3/6 or 1/2, and the probability of rolling a 1 is 1/6. Therefore, the probability of all three events occurring is (1/6) * (1/2) * (1/6) = 1/108.
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5.
Landing on heads after tossing a coin and rolling a 5 on a single 6-sided die
A.
Independent Events
B.
Dependent Events
Correct Answer A. Independent Events
Explanation The landing on heads after tossing a coin and rolling a 5 on a single 6-sided die are independent events because the outcome of one event does not affect the outcome of the other event. Tossing a coin and rolling a die are unrelated actions, and the probability of landing on heads or rolling a 5 does not change based on the outcome of the other event. Therefore, these events can be considered independent.
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6.
A bag contains 3 red cubes, 4 green cubes, and 5 blue cubes. One cube is taken from the bag and is not replaced. Another cube is taken.
A.
Dependent
B.
Independent
Correct Answer A. Dependent
Explanation The answer is dependent because the probability of selecting the second cube is affected by the outcome of the first selection. Since the first cube is not replaced, the number of cubes of each color in the bag changes after each selection. Therefore, the probability of selecting a particular color cube on the second draw depends on the color of the cube selected on the first draw.
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7.
Spinning a number 6 and then spinning a number 5 on the same spinner.
A.
Independent Events
B.
Dependent Events
Correct Answer A. Independent Events
Explanation The spinning of a number 6 and then a number 5 on the same spinner are independent events because the outcome of spinning a number 6 does not affect the probability or outcome of spinning a number 5. Each spin is completely unrelated to the other and the outcome of one does not depend on the outcome of the other.
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8.
A spinner numbered 1 through 10 is spun 100 times. The results of the experiment are shown in the table below. What is the experimental probability of spinning an 8?
A.
7/100
B.
1/100
C.
13/100
D.
10/100
Correct Answer C. 13/100
Explanation The experimental probability of spinning an 8 is 13/100 because out of the 100 spins, the number 8 appeared 13 times.
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9.
A set of 15 cards is numbered 1, 2, 3, …, 15. Suppose you choose one card at random without looking. What is the probability of choosing an odd-numbered card?
A.
1/2
B.
7/15
C.
1/15
D.
8/15
Correct Answer D. 8/15
Explanation When choosing a card at random from a set of 15 cards numbered 1 to 15, there are 8 odd-numbered cards (1, 3, 5, 7, 9, 11, 13, 15) and 15 total cards. Therefore, the probability of choosing an odd-numbered card is 8/15.
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10.
From left to right on the number line, order the events based on how likely they are to occur.a. The event is certain to happen.b. The event is just as likely to happen as not to happen.c. The event has no chance of happening.d. The event could happen but is unlikely.e. The event is likely to happen.
A.
A, e, b, d, c
B.
D, c, b, e, a
C.
D, c, b, a, e
D.
C, d, b, e, a
Correct Answer D. C, d, b, e, a
Explanation The events are ordered based on their likelihood of occurring. The event with no chance of happening is the least likely (c), followed by an event that could happen but is unlikely (d). The event that is just as likely to happen as not to happen is next (b), followed by an event that is likely to happen (e). The event that is certain to happen is the most likely (a).
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11.
Something that is unlikely to happen has a probability of between
A.
1 and 2
B.
0.5 and 1
C.
0 and 0.5
Correct Answer C. 0 and 0.5
Explanation Something that is unlikely to happen has a probability of between 0 and 0.5. This means that the chances of it occurring are less than 50%. The closer the probability is to 0, the more unlikely the event is to happen. Therefore, a probability between 0 and 0.5 accurately represents something that is unlikely to occur.
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12.
A bag contains just 5 buttons, all of which are blue. What is the probability of picking a red button from the bag?
A.
0.5
B.
1
C.
0
Correct Answer C. 0
Explanation Since the bag only contains blue buttons, there are no red buttons to pick from. Therefore, the probability of picking a red button from the bag is 0.
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13.
A bag contains 4 white buttons. How many black buttons must be added so there is an even chance of picking a white button?
A.
8
B.
4
C.
2
D.
0
Correct Answer B. 4
Explanation To have an even chance of picking a white button, the number of white buttons and black buttons must be equal. Since there are initially 4 white buttons in the bag, we need to add 4 black buttons to make the total number of buttons 8. This way, there will be an even chance of picking a white button (4 out of 8) or a black button (4 out of 8). Therefore, the correct answer is 4.
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14.
You have 15 pennies in your pocket. Of those pennies, 3 are Canadian. Suppose you pick a penny out of your pocket at random. Find P(not Canadian). This is a ___________________________event.
Correct Answer likely
Explanation This is a likely event because there are 15 pennies in total and only 3 of them are Canadian. Therefore, the probability of picking a penny that is not Canadian is high.
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15.
M A T H E M A T I C S ( Each letter represents a card)You select a card at random. Without replacing the card, you select a second card. Find the probability. P(M, then H)
Correct Answer 1/55
Explanation The probability of selecting the letter M on the first card is 1/11 because there is only one M card out of a total of 11 cards. After selecting the first card, there are now 10 cards left, and the probability of selecting the letter H on the second card is 1/10 because there is only one H card left. Since these two events are independent, we can multiply the probabilities together to get (1/11) * (1/10) = 1/110. However, the question states that the cards are not replaced, so the denominator should be adjusted to 11 * 10 instead of 11 * 11, resulting in a final probability of 1/110 * 11/10 = 1/55.
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