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 = 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice= 4
P =
2.Easy
sum ≥ 7die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 7?

2 dice≥ 7
P =
3.Medium
xp(x)00.320.2540.260.25μ = 2.8

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

x: 0, 2, 4, 6p(x): 0.3, 0.25, 0.2, 0.25
σ =
4.Medium
red: 7blue: 8

A bag holds 7 red and 8 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 8
P =
5.Hard
xp(x)00.210.2520.2530.3μ

X has the distribution shown, and Y = 0.5X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.2, 0.25, 0.25, 0.3Y = 0.5X + 1
σY =
6.Hard
€p(x)−20.860.15180.05

A game costs €2 to play. You win €8 with probability 0.15 and €20 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€8: p = 0.15€20: p = 0.05
E(G) = €

Answer key

  1. 1. P = 0.08333
  2. 2. P = 0.5833
  3. 3. σ = 2.315
  4. 4. P = 0.2
  5. 5. σY = 0.554
  6. 6. E(G) = 0.2 €

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