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
xp(x)10.0520.3530.0540.350.25

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

x: 1, 2, 3, 4, 5p(x): 0.05, 0.35, 0.05, 0.3, 0.25
E(X) =
3.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
Var(X) =
4.Medium
red: 3blue: 7

A bag holds 3 red and 7 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 7
P =
5.Hard
n = 7, p = 0.25: P(X = 2) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 2 correct answers?

n = 7p = 0.25k = 2
P =
6.Hard
€p(x)−30.8990.11470.01

A game costs €3 to play. You win €12 with probability 0.1 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 = 0.1€150: p = 0.01
E(G) = €

Answer key

  1. 1. P = 0.8333
  2. 2. E(X) = 3.35
  3. 3. Var(X) = 0.6475
  4. 4. P = 0.06667
  5. 5. P = 0.3115
  6. 6. E(G) = −0.3 €

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