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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1.Easy
sum = 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 11?

2 dice= 11
P =
2.Easy
sum = 10die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice= 10
P =
3.Medium
xp(x)10.2520.0530.1540.2550.3μ = 3.3

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

x: 1, 2, 3, 4, 5p(x): 0.25, 0.05, 0.15, 0.25, 0.3
σ =
4.Medium
red: 8blue: 9

A bag holds 8 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

8 / 9
P =
5.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = 2X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = 2X + 1
σY =
6.Hard
n = 8, p = 0.5: P(X = 1) = ?k012345678

A test has 8 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 1 correct answers?

n = 8p = 0.5k = 1
P =

Answer key

  1. 1. P = 0.05556
  2. 2. P = 0.08333
  3. 3. σ = 1.552
  4. 4. P = 0.2059
  5. 5. σY = 1.673
  6. 6. P = 0.03125

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