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
red: 5blue: 3green: 1

A bag holds 5 red, 3 blue and 1 green balls. You draw one at random. What is the probability P that it is not red?

5 / 3 / 1
P =
2.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 =
3.Medium
xp(x)00.320.240.360.2μ = 2.8

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

x: 0, 2, 4, 6p(x): 0.3, 0.2, 0.3, 0.2
σ =
4.Medium
xp(x)100.35200.35300.25400.05μ = 20

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

x: 10, 20, 30, 40p(x): 0.35, 0.35, 0.25, 0.05
Var(X) =
5.Hard
€p(x)−50.8450.152450.01

A game costs €5 to play. You win €10 with probability 0.15 and €250 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€10: p = 0.15€250: p = 0.01
E(G) = €
6.Hard
xp(x)00.310.220.1530.35μ

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

x: 0, 1, 2, 3p(x): 0.3, 0.2, 0.15, 0.35Y = 5X + 10
σY =

Answer key

  1. 1. P = 0.4444
  2. 2. P = 0.1111
  3. 3. σ = 2.227
  4. 4. Var(X) = 80
  5. 5. E(G) = −1 €
  6. 6. σY = 6.22

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