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: 8green: 4

A bag holds 8 red, 8 blue and 4 green balls. You draw one at random. What is the probability P that it is blue?

8 / 8 / 4
P =
2.Easy
red: 7blue: 7green: 3

A bag holds 7 red, 7 blue and 3 green balls. You draw one at random. What is the probability P that it is not red?

7 / 7 / 3
P =
3.Medium
xp(x)00.220.3540.3560.1μ = 2.7

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

x: 0, 2, 4, 6p(x): 0.2, 0.35, 0.35, 0.1
Var(X) =
4.Medium
xp(x)00.320.340.1560.25μ = 2.7

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

x: 0, 2, 4, 6p(x): 0.3, 0.3, 0.15, 0.25
σ =
5.Hard
xp(x)00.310.320.0530.35μ

X has the distribution shown, and Y = 5X + 5. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.3, 0.3, 0.05, 0.35Y = 5X + 5
σY =
6.Hard
n = 9, p = 0.1: P(X ≤ 1) = ?k0123456789

9 components are tested, and each one fails with probability 0.1, independently. What is the probability P that at most one fails?

n = 9p = 0.1
P =

Answer key

  1. 1. P = 0.4
  2. 2. P = 0.5882
  3. 3. Var(X) = 3.31
  4. 4. σ = 2.304
  5. 5. σY = 6.22
  6. 6. P = 0.7748

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