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: 7blue: 6green: 4

A bag holds 7 red, 6 blue and 4 green balls. You draw one at random. What is the probability P that it is not red?

7 / 6 / 4
P =
2.Easy
sum ≥ 5die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 5?

2 dice≥ 5
P =
3.Medium
xp(x)00.3510.320.35μ = 1

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
σ =
4.Medium
n = 12k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 12? The order does not matter.

n = 12k = 3
N =
5.Hard
n = 10, p = 0.7: P(X ≤ 1) = ?k012345678910

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

n = 10p = 0.7
P =
6.Hard
xp(x)00.210.320.3530.0540.1μ

X has the distribution shown, and Y = −2X + 4. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.2, 0.3, 0.35, 0.05, 0.1Y = −2X + 4
σY =

Answer key

  1. 1. P = 0.5882
  2. 2. P = 0.8333
  3. 3. σ = 0.8367
  4. 4. N = 220
  5. 5. P = 0.0001437
  6. 6. σY = 2.322

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