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 = 5die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 5?

2 dice= 5
P =
2.Easy
red: 2blue: 7green: 2

A bag holds 2 red, 7 blue and 2 green balls. You draw one at random. What is the probability P that it is not red?

2 / 7 / 2
P =
3.Medium
xp(x)10.0520.330.340.35μ = 2.95

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

x: 1, 2, 3, 4p(x): 0.05, 0.3, 0.3, 0.35
σ =
4.Medium
xp(x)00.3510.120.230.35μ = 1.55

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

x: 0, 1, 2, 3p(x): 0.35, 0.1, 0.2, 0.35
Var(X) =
5.Hard
xp(x)00.2510.320.3530.1μ

X has the distribution shown, and Y = 5X + 20. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.25, 0.3, 0.35, 0.1Y = 5X + 20
σY =
6.Hard
€p(x)−10.7440.25190.01

A game costs €1 to play. You win €5 with probability 0.25 and €20 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€5: p = 0.25€20: p = 0.01
E(G) = €

Answer key

  1. 1. P = 0.1111
  2. 2. P = 0.8182
  3. 3. σ = 0.9206
  4. 4. Var(X) = 1.648
  5. 5. σY = 4.77
  6. 6. E(G) = 0.45 €

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