Probability Practice Problems

1. On a six-sided die, each side has a number between 1 and 6. What is the probability of throwing a 3 or a 4?
  1. 1 in 6
  2. 1 in 3
  3. 1 in 2
  4. 1 in 4
2. Three coins are tossed up in the air, one at a time. What is the probability that two of them will land heads up and one will land tails up?
  1. 0
  2. 1/8
  3. 1/4
  4. 3/8
3. A two-digit number is chosen at random. What is the probability that the chosen number is a multiple of 7?
  1. 1/10
  2. 1/9
  3. 11/90
  4. 12/90
  5. 13/90
4. A bag contains 14 blue, 6 red, 12 green, and 8 purple buttons. 25 buttons are removed from the bag randomly. How many of the removed buttons were red if the chance of drawing a red button from the bag is now 1/3?
  1. 0
  2. 1
  3. 3
  4. 5
  5. 6
5. There are 6 blue marbles, 3 red marbles, and 5 yellow marbles in a bag. What is the probability of selecting a blue or red marble on the first draw?
  1. 1/3
  2. 4/7
  3. 8/14
  4. 9/14
  5. 11/14
6. Using a six-sided die, Carlin has rolled a six on each of 4 successive tosses. What is the probability of Carlin rolling a six on the next toss?
  1. 1/2
  2. 1/4
  3. 1/6
  4. 1/30
  5. 1/3125
7. A regular deck of cards has 52 cards. Assuming that you do not replace the card you had drawn before the next draw, what is the probability of drawing three aces in a row?
  1. 1 in 52
  2. 1 in 156
  3. 1 in 2000
  4. 1 in 5525
  5. 1 in 132600
8. An MP3 player is set to play songs at random from the fifteen songs it contains in memory. Any song can be played at any time, even if it is repeated. There are 5 songs by Band A, 3 songs by Band B, 2 by Band C, and 5 by Band D. If the player has just played two songs in a row by Band D, what is the probability that the next song will also be by Band D?
  1. 1 in 5
  2. 1 in 3
  3. 1 in 9
  4. 1 in 27
  5. Not enough data to determine.
9. Referring again to the MP3 player described in Question 8, what is the probability that the next two songs will both be by Band B?
  1. 1 in 25
  2. 1 in 3
  3. 1 in 5
  4. 1 in 9
  5. Not enough data to determine.
10. If a bag of balloons consists of 47 white balloons, 5 yellow balloons, and 10 black balloons, what is the approximate likelihood that a balloon chosen randomly from the bag will be black?
  1. 19%
  2. 16%
  3. 21%
  4. 33%
11. In a lottery game, there are 2 winners for every 100 tickets sold. If a man buys 10 tickets, what are the chances that he is a winner?
  1. 1 in 2
  2. 1 in 5
  3. 2 in 5
  4. 2 in 2

 

Answers and Explanations


1. B: On a six-sided die, the probability of throwing any number is 1 in 6. The probability of throwing a 3 or a 4 is double that, or 2 in 6. This can be simplified by dividing both 2 and 6 by 2.

Therefore, the probability of throwing either a 3 or 4 is 1 in 3.

2. D: Shown below is the sample space of possible outcomes for tossing three coins, one at a time. Since there is a possibility of two outcomes (heads or tails) for each coin, there is a total of 2*2*2=8 possible outcomes for the three coins altogether. Note that H represents heads and T represents tails:

HHH HHT HTT HTH TTT TTH THT THH

Notice that out of the 8 possible outcomes, only 3 of them (HHT, HTH, and THH) meet the desired condition that two coins land heads up and one coin lands tails up. Probability, by definition, is the number of desired outcomes divided by the number of possible outcomes. Therefore, the probability of two heads and one tail is 3/8, Choice D.

3. E: There are 90 two-digit numbers (all integers from 10 to 99). Of those, there are 13 multiples of 7: 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98.

4. B: Add the 14 blue, 6 red, 12 green, and 8 purple buttons to get a total of 40 buttons. If 25 buttons are removed, there are 15 buttons remaining in the bag. If the chance of drawing a red button is now 1/3, then 5 of the 15 buttons remaining must be red. The original total of red buttons was 6. So, one red button was removed.

5. D: Use this ratio for probability:

Probability = Number of Desired Outcomes

Number of Possible Outcomes

There are 6 blue marbles and 3 red marbles for a total of 9 desired outcomes. Add the total number of marbles to get the total number of possible outcomes, 14. The probability that a red or blue marble will be selected is 9/14.

6. C: The outcomes of previous rolls do not affect the outcomes of future rolls. There is one desired outcome and six possible outcomes. The probability of rolling a six on the fifth roll is 1/6, the same as the probability of rolling a six on any given individual roll.

7. D: The probability of getting three aces in a row is the product of the probabilities for each draw. For the first ace, that is 4 in 52 or 1 in 13; for the second, it is 3 in 51 or 1 in 27; and for the third, it is 2 in 50 or 1 in 25. So the overall probability, P, is P=1/13*1/17*1/25=1/5,525

8. B: The probability of playing a song by a particular band is proportional to the number of songs by that band divided by the total number of songs, or 5/15=1/3 for B and D. The probability of playing any particular song is not affected by what has been played previously, since the choice is random and songs may be repeated.

9. A: Since 3 of the 15 songs are by Band B, the probability that any one song will be by that band is 3/15=1/5. The probability that the next two songs are by Band B is equal to the product of two probabilities, where each probability is that the next song is by Band B: 1/5*1/5=1/25 The same probability of 1/5 may be multiplied twice because whether or not the first song is by Band B has no impact on whether the second song is by Band B. They are independent events.

10. B: First, calculate the total number of balloons in the bag: 47 + 5 + 10 = 62.

Ten of these are black, so divide this number by 62. Then, multiply by 100 to express the probability as a percentage:

10 / 62 = 0.16

0.16 100 = 16%

11. B: First, it is easier to work this problem if we find out how many tickets are sold for there to be one winner. If there are 2 winners for every 100 tickets, there is 1 winner for every 50 tickets sold.

Therefore, if he buys ten tickets, the chances of winning are 10 in 50.

This can also be expressed as 1 in 5.