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 = 8die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 8?

2 dice= 8
P =
2.Easy
xp(x)00.3510.3520.3

A random variable X has the probability distribution shown. Find its expected value E(X).

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
E(X) =
3.Medium
P(at least one six) = ??1?2?3?4P(six) = 1/6 on each roll

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
4.Medium
xp(x)00.210.3520.130.35μ = 1.6

For the distribution shown, find the standard deviation σ of X.

x: 0, 1, 2, 3p(x): 0.2, 0.35, 0.1, 0.35
σ =
5.Hard
n = 5, p = 0.25: P(X ≤ 1) = ?k012345

5 components are tested, and each one fails with probability 0.25, independently. What is the probability P that at most one fails?

n = 5p = 0.25
P =
6.Hard
n = 7, p = 0.5: P(X ≤ 1) = ?k01234567

7 components are tested, and each one fails with probability 0.5, independently. What is the probability P that at most one fails?

n = 7p = 0.5
P =

Answer key

  1. 1. P = 0.1389
  2. 2. E(X) = 0.95
  3. 3. P = 0.5177
  4. 4. σ = 1.158
  5. 5. P = 0.6328
  6. 6. P = 0.0625

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