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 = 8die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 8?

2 dice= 8
P =
2.Easy
red: 2blue: 3green: 5

A bag holds 2 red, 3 blue and 5 green balls. You draw one at random. What is the probability P that it is not red?

2 / 3 / 5
P =
3.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
Var(X) =
4.Medium
xp(x)10.3520.0530.1540.2550.2μ = 2.9

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

x: 1, 2, 3, 4, 5p(x): 0.35, 0.05, 0.15, 0.25, 0.2
σ =
5.Hard
€p(x)−100.79400.2900.01

A game costs €10 to play. You win €50 with probability 0.2 and €100 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€50: p = 0.2€100: p = 0.01
E(G) = €
6.Hard
xp(x)00.2510.320.230.25μ

X has the distribution shown, and Y = 0.5X + 10. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.25, 0.3, 0.2, 0.25Y = 0.5X + 10
σY =

Answer key

  1. 1. P = 0.1389
  2. 2. P = 0.8
  3. 3. Var(X) = 0.6475
  4. 4. σ = 1.578
  5. 5. E(G) = 1 €
  6. 6. σY = 0.5585

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