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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1.Easy
sum ≥ 10die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 10?

2 dice≥ 10
P =
2.Easy
xp(x)0?20.2540.360.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 2, 4, 6p(x): ?, 0.25, 0.3, 0.35
P(X = 0) =
3.Medium
red: 6blue: 4

A bag holds 6 red and 4 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

6 / 4
P =
4.Medium
P(at least one six) = ??1?2P(six) = 1/6 on each roll

A fair die is rolled 2 times. What is the probability P of getting at least one six?

n = 2
P =
5.Hard
€p(x)−10.8910.1190.01

A game costs €1 to play. You win €2 with probability 0.1 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€2: p = 0.1€20: p = 0.01
E(G) = €
6.Hard
€p(x)−30.7490.251470.01

A game costs €3 to play. You win €12 with probability 0.25 and €150 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€12: p = 0.25€150: p = 0.01
E(G) = €

Answer key

  1. 1. P = 0.1667
  2. 2. P(X = 0) = 0.1
  3. 3. P = 0.3333
  4. 4. P = 0.3056
  5. 5. E(G) = −0.6 €
  6. 6. E(G) = 1.5 €

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