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 at least 5?

2 dice≥ 5
P =
2.Easy
red: 8blue: 2green: 1

A bag holds 8 red, 2 blue and 1 green balls. You draw one at random. What is the probability P that it is not red?

8 / 2 / 1
P =
3.Medium
red: 7blue: 6

A bag holds 7 red and 6 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 6
P =
4.Medium
xp(x)10.0520.2530.340.1550.25μ = 3.3

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

x: 1, 2, 3, 4, 5p(x): 0.05, 0.25, 0.3, 0.15, 0.25
σ =
5.Hard
xp(x)10.320.130.0540.3550.2μ

X has the distribution shown, and Y = −2X + 1. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.3, 0.1, 0.05, 0.35, 0.2Y = −2X + 1
σY =
6.Hard
€p(x)−30.7830.2570.02

A game costs €3 to play. You win €6 with probability 0.2 and €60 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€6: p = 0.2€60: p = 0.02
E(G) = €

Answer key

  1. 1. P = 0.8333
  2. 2. P = 0.2727
  3. 3. P = 0.2692
  4. 4. σ = 1.229
  5. 5. σY = 3.129
  6. 6. E(G) = −0.6 €

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