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 exactly 5?

2 dice= 5
P =
2.Easy
xp(x)100.3200.15300.3400.25

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

x: 10, 20, 30, 40p(x): 0.3, 0.15, 0.3, 0.25
E(X) =
3.Medium
xp(x)10.1520.3530.340.2μ = 2.55

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

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

A bag holds 3 red and 5 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 5
P =
5.Hard
n = 10, p = 0.5: P(X ≤ 1) = ?k012345678910

10 components are tested, and each one fails with probability 0.5, independently. What is the probability P that at most one fails?

n = 10p = 0.5
P =
6.Hard
€p(x)−50.83150.15450.02

A game costs €5 to play. You win €20 with probability 0.15 and €50 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€20: p = 0.15€50: p = 0.02
E(G) = €

Answer key

  1. 1. P = 0.1111
  2. 2. E(X) = 25
  3. 3. Var(X) = 0.9475
  4. 4. P = 0.1071
  5. 5. P = 0.01074
  6. 6. E(G) = −1 €

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