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 at least 8?

2 dice≥ 8
P =
2.Easy
xp(x)00.1510.320.330.25

A random variable X has the probability distribution shown. Find its expected value E(X).

x: 0, 1, 2, 3p(x): 0.15, 0.3, 0.3, 0.25
E(X) =
3.Medium
red: 3blue: 6

A bag holds 3 red and 6 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 6
P =
4.Medium
xp(x)00.210.320.230.3μ = 1.6

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

x: 0, 1, 2, 3p(x): 0.2, 0.3, 0.2, 0.3
Var(X) =
5.Hard
€p(x)−20.760.25980.05

A game costs €2 to play. You win €8 with probability 0.25 and €100 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€8: p = 0.25€100: p = 0.05
E(G) = €
6.Hard
€p(x)−20.8940.1980.01

A game costs €2 to play. You win €6 with probability 0.1 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 = €2€6: p = 0.1€100: p = 0.01
E(G) = €

Answer key

  1. 1. P = 0.4167
  2. 2. E(X) = 1.65
  3. 3. P = 0.08333
  4. 4. Var(X) = 1.24
  5. 5. E(G) = 5 €
  6. 6. E(G) = −0.4 €

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