Probability worksheet with answers

Free printable Probability worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
sum = 10die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 10?

2 dice= 10
P =
2.Easy
xp(x)10.120.23?40.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 1, 2, 3, 4p(x): 0.1, 0.2, ?, 0.35
P(X = 3) =
3.Medium
P(at least one six) = ??1?2?3?4?5?6?7P(six) = 1/6 on each roll

A fair die is rolled 7 times. What is the probability P of getting at least one six?

n = 7
P =
4.Medium
n = 13k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 13? The order does not matter.

n = 13k = 4
N =
5.Hard
n = 7, p = 0.2: P(X = 5) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 5 correct answers?

n = 7p = 0.2k = 5
P =
6.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = −2X + 10. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = −2X + 10
σY =

Answer key

  1. 1. P = 0.08333
  2. 2. P(X = 3) = 0.35
  3. 3. P = 0.7209
  4. 4. N = 715
  5. 5. P = 0.004301
  6. 6. σY = 1.673

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