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
sum ≥ 8die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice≥ 8
P =
2.Easy
red: 7blue: 2green: 4

A bag holds 7 red, 2 blue and 4 green balls. You draw one at random. What is the probability P that it is not red?

7 / 2 / 4
P =
3.Medium
xp(x)10.2520.330.240.25μ = 2.45

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

x: 1, 2, 3, 4p(x): 0.25, 0.3, 0.2, 0.25
σ =
4.Medium
red: 3blue: 6

A bag holds 3 red and 6 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 6
P =
5.Hard
n = 5, p = 0.1: P(X = 1) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 1 correct answers?

n = 5p = 0.1k = 1
P =
6.Hard
n = 11, p = 0.2: P(X ≤ 1) = ?k01234567891011

11 components are tested, and each one fails with probability 0.2, independently. What is the probability P that at most one fails?

n = 11p = 0.2
P =

Answer key

  1. 1. P = 0.4167
  2. 2. P = 0.4615
  3. 3. σ = 1.117
  4. 4. P = 0.08333
  5. 5. P = 0.3281
  6. 6. P = 0.3221

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