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 = 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
xp(x)10.052?30.3540.25

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 1, 2, 3, 4p(x): 0.05, ?, 0.35, 0.25
P(X = 2) =
3.Medium
xp(x)10.1520.2530.3540.150.15μ = 2.85

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

x: 1, 2, 3, 4, 5p(x): 0.15, 0.25, 0.35, 0.1, 0.15
σ =
4.Medium
red: 6blue: 3

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

6 / 3
P =
5.Hard
xp(x)10.220.130.3540.250.15μ

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

x: 1, 2, 3, 4, 5p(x): 0.2, 0.1, 0.35, 0.2, 0.15Y = −2X + 1
σY =
6.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = 3X + 4. Find the standard deviation σY of Y.

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

Answer key

  1. 1. P = 0.05556
  2. 2. P(X = 2) = 0.35
  3. 3. σ = 1.236
  4. 4. P = 0.4167
  5. 5. σY = 2.608
  6. 6. σY = 2.51

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