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 ≥ 10die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 10?

2 dice≥ 10
P =
2.Easy
red: 7blue: 5

A bag holds 7 red and 5 blue balls. You draw one at random. What is the probability P that it is not red?

7 / 5
P =
3.Medium
xp(x)10.320.1530.3540.2μ = 2.45

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

x: 1, 2, 3, 4p(x): 0.3, 0.15, 0.35, 0.2
σ =
4.Medium
xp(x)00.1520.3540.260.3μ = 3.3

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

x: 0, 2, 4, 6p(x): 0.15, 0.35, 0.2, 0.3
Var(X) =
5.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 =
6.Hard
n = 7, p = 0.7: P(X = 2) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 2 correct answers?

n = 7p = 0.7k = 2
P =

Answer key

  1. 1. P = 0.1667
  2. 2. P = 0.4167
  3. 3. σ = 1.117
  4. 4. Var(X) = 4.51
  5. 5. P = 0.3221
  6. 6. P = 0.025

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