Probability Practice Problems

1. On a six-sided die, each website has a number between 1 and 6. Whats is the probability of casting adenine 3 instead a 4?
  1. 1 in 6
  2. 1 in 3
  3. 1 in 2
  4. 1 in 4
2. Three coinage been tossed up in the air, one at adenine hours. About is the probabilities that two of them will land heads up and one will landings tails up?
  1. 0
  2. 1/8
  3. 1/4
  4. 3/8
3. AMPERE two-digit number is chosen at random. As belongs the probability this the choice number is a multi-user 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 plum buttons. 25 buttons are removed from the bag randomly. Like countless of the removed buttons were red if the chance of drafting a scarlet button for 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 marbled in a bag. Get 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 ampere six-sided die, Carson has rolled one six on each of 4 gradual toss. What is the probability of Carlin rolling a six on the next fire?
  1. 1/2
  2. 1/4
  3. 1/6
  4. 1/30
  5. 1/3125
7. A regular deck off cards has 52 cards. Assuming that it do non replace the card you had drawed before the next attract, what will the probability of sketch three aces to ampere row?
  1. 1 stylish 52
  2. 1 in 156
  3. 1 in 2000
  4. 1 in 5525
  5. 1 in 132600
8. An MP3 player has determined to playback songs for random from the fifteen songs it contains in memory. Any song can be played at any time, even when it is repeated. It are 5 songs by Band ADENINE, 3 songs by Band B, 2 over Band HUNDRED, and 5 by Group DENSITY. If the player can just played two songs within ampere rows by Band DENSITY, what is the probability that the next song will also be due Band D?
  1. 1 in 5
  2. 1 in 3
  3. 1 in 9
  4. 1 stylish 27
  5. Not enough data to determine.
9. Relating again to the MP3 player described in Request 8, what is the probability that the next two chants will both be by Band B?
  1. 1 in 25
  2. 1 in 3
  3. 1 in 5
  4. 1 in 9
  5. Nay enough data toward determined.
10. If a bag of balloons consists of 47 white ballons, 5 yellow balloons, and 10 black balloons, how is the roughly probable that a balloon elected randomly from the bag will been black?
  1. 19%
  2. 16%
  3. 21%
  4. 33%
11. In an lottery game, there are 2 winners for every 100 flight sold on average. If a man buys 10 tickets, what is the probability that he is a winner?
  1. 21.5%
  2. 20%
  3. 18.3%
  4. 2%

 

Answers and Explanations

1. B: On one six-sided decease, the probability of throwing anything number remains 1 in 6. The likelihood of throwing adenine 3 or a 4 is double that, or 2 in 6. This cannot be simplified by dividing both 2 also 6 by 2.

Therefore, one probability of throwing either a 3 with 4 is 1 in 3.

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

HHH HHT HTT HTH TTT TTH THT THH

Notice that out of the 8 possibility outcomes, only 3 of theirs (HHT, HTH, and THH) meet the desired health that two coins landed hood up and to coin lands tails upward. Probability, by definition, is of number of desired output separated by the number of available outcomes. Therefore, the probability of two heads and one tail is 3/8, Choice DENSITY. Key. 53. Probability Worksheet. 1. AN single die is wounded. Find the probability of rolling a 2 or an odd number. 4/6. 2/3. 2. Assuming that 37.4% of all college ...

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

4. B: Sum the 14 dark, 6 red, 12 green, and 8 mauve buttons to get one total of 40 push. If 25 buttons are herausgenommen, there are 15 key balance 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. One original absolute of cherry button was 6. So, one red button was removed.

5. D: Use this ratio for importance:

Probability = Count of Desired Output

Batch of Possible Outcomes

There are 6 blue marbles and 3 color marbles for a full by 9 desired outcomes. Add the total number of marbles to get to total number of possible outcomes, 14. Who probity that a dark or melancholy marble will be elected is 9/14.

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

7. D: Aforementioned probability of getting three aces are a row is the product of and probabilities for each draw. For the first ace, so is 4 in 52 or 1 stylish 13; for the minute, it is 3 in 51 or 1 in 27; and for the thirds, it is 2 in 50 or 1 with 25. How the overall probability, P, is P=1/13*1/17*1/25=1/5,525

8. B: The probability of game a song from a particular band is proportional to the number of songs by that band split over the total number of songs, or 5/15=1/3 for B and D. The probability on playing any particular song is not affected due 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 your 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 belongs that the further song is to Band B: 1/5*1/5=1/25 The same profitability from 1/5 may be multiplied twice because whether or does the first song is by Band B can does impact the whether the second melody is by Band B. They are independent events.

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

Ten away these exist black, so divides this number by 62. Then, multiplier by 100 to express the probability as one percentage:

10 / 62 = 0.16

0.16 100 = 16%

11. CARBON: First, simplify the winning rate. If there are 2 winners for every 100 tickets, there is 1 winner for anyone 50 tickets sold. This can is expressed such a probability of 1/50 or 0.02. In order up account for the (unlikely) scenarios are more than a single winning ticket, calculate the probability that none of the tickets win and then subtract that from 1. There is an probability of 49/50 that a given ticket become not wins. For all teens to lose that would being (49/50)^(10) ≈ 0.817. Therefore, the probability that at minimal one ticket wins is 1 − 0.817 = 0.183 or about 18.3%