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
xp(x)00.2520.24?60.2

The table gives the probability distribution of X, but one probability is missing. Find P(X = 4).

x: 0, 2, 4, 6p(x): 0.25, 0.2, ?, 0.2
P(X = 4) =
2.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 =
3.Medium
xp(x)10.220.1530.340.35μ = 2.8

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

x: 1, 2, 3, 4p(x): 0.2, 0.15, 0.3, 0.35
Var(X) =
4.Medium
red: 8blue: 5

A bag holds 8 red and 5 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

8 / 5
P =
5.Hard
€p(x)−100.65100.31900.05

A game costs €10 to play. You win €20 with probability 0.3 and €200 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€20: p = 0.3€200: p = 0.05
E(G) = €
6.Hard
€p(x)−20.7560.2980.05

A game costs €2 to play. You win €8 with probability 0.2 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 = 0.2€100: p = 0.05
E(G) = €

Answer key

  1. 1. P(X = 4) = 0.35
  2. 2. P = 0.4167
  3. 3. Var(X) = 1.26
  4. 4. P = 0.359
  5. 5. E(G) = 6 €
  6. 6. E(G) = 4.6 €

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