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: 4blue: 6green: 3

A bag holds 4 red, 6 blue and 3 green balls. You draw one at random. What is the probability P that it is red?

4 / 6 / 3
P =
2.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 =
3.Medium
xp(x)00.310.3520.35μ = 1.05

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
σ =
4.Medium
xp(x)00.110.320.2530.2540.1μ = 1.95

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

x: 0, 1, 2, 3, 4p(x): 0.1, 0.3, 0.25, 0.25, 0.1
Var(X) =
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
xp(x)10.2520.2530.2540.0550.2μ

X has the distribution shown, and Y = 3X + 20. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.25, 0.25, 0.25, 0.05, 0.2Y = 3X + 20
σY =

Answer key

  1. 1. P = 0.3077
  2. 2. P = 0.1389
  3. 3. σ = 0.8047
  4. 4. Var(X) = 1.347
  5. 5. P = 4.724 × 10⁻⁵
  6. 6. σY = 4.253

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