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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Name: ____________________   Date: ____________

1.Easy
red: 8blue: 2

A bag holds 8 red and 2 blue balls. You draw one at random. What is the probability P that it is not red?

8 / 2
P =
2.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 =
3.Medium
xp(x)00.2510.2520.1530.35μ = 1.6

For the distribution shown, find the variance Var(X) of X.

x: 0, 1, 2, 3p(x): 0.25, 0.25, 0.15, 0.35
Var(X) =
4.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 =
5.Hard
n = 11, p = 0.7: P(X ≤ 1) = ?k01234567891011

11 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 11p = 0.7
P =
6.Hard
n = 6, p = 0.7: P(X ≤ 1) = ?k0123456

6 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 6p = 0.7
P =

Answer key

  1. 1. P = 0.2
  2. 2. P = 0.08333
  3. 3. Var(X) = 1.44
  4. 4. P = 0.7209
  5. 5. P = 4.724 × 10⁻⁵
  6. 6. P = 0.01094

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