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 = 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 11?

2 dice= 11
P =
2.Easy
sum = 9die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 9?

2 dice= 9
P =
3.Medium
xp(x)00.2510.2520.330.140.1μ = 1.55

For the distribution shown, find the standard deviation σ of X.

x: 0, 1, 2, 3, 4p(x): 0.25, 0.25, 0.3, 0.1, 0.1
σ =
4.Medium
red: 5blue: 8

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

5 / 8
P =
5.Hard
€p(x)−50.68150.32450.02

A game costs €5 to play. You win €20 with probability 0.3 and €250 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 = 0.3€250: p = 0.02
E(G) = €
6.Hard
n = 12, p = 0.25: P(X ≤ 1) = ?k0123456789101112

12 components are tested, and each one fails with probability 0.25, independently. What is the probability P that at most one fails?

n = 12p = 0.25
P =

Answer key

  1. 1. P = 0.05556
  2. 2. P = 0.1111
  3. 3. σ = 1.244
  4. 4. P = 0.1282
  5. 5. E(G) = 6 €
  6. 6. P = 0.1584

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