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 ≥ 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 4?

2 dice≥ 4
P =
2.Easy
sum ≥ 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice≥ 11
P =
3.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 =
4.Medium
red: 5blue: 4

A bag holds 5 red and 4 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

5 / 4
P =
5.Hard
xp(x)00.310.120.230.340.1μ

X has the distribution shown, and Y = 5X + 10. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.3, 0.1, 0.2, 0.3, 0.1Y = 5X + 10
σY =
6.Hard
xp(x)00.3510.320.1530.2μ

X has the distribution shown, and Y = 5X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.35, 0.3, 0.15, 0.2Y = 5X + 1
σY =

Answer key

  1. 1. P = 0.9167
  2. 2. P = 0.08333
  3. 3. P = 0.4167
  4. 4. P = 0.2778
  5. 5. σY = 7
  6. 6. σY = 5.612

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