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 ≥ 3die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 3?

2 dice≥ 3
P =
2.Easy
xp(x)00.3520.3540.260.1

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

x: 0, 2, 4, 6p(x): 0.35, 0.35, 0.2, 0.1
E(X) =
3.Medium
n = 11k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 11? The order does not matter.

n = 11k = 5
N =
4.Medium
n = 11k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 11? The order does not matter.

n = 11k = 3
N =
5.Hard
n = 10, p = 0.4: P(X ≤ 1) = ?k012345678910

10 components are tested, and each one fails with probability 0.4, independently. What is the probability P that at most one fails?

n = 10p = 0.4
P =
6.Hard
€p(x)−100.78300.24900.02

A game costs €10 to play. You win €40 with probability 0.2 and €500 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€40: p = 0.2€500: p = 0.02
E(G) = €

Answer key

  1. 1. P = 0.9722
  2. 2. E(X) = 2.1
  3. 3. N = 462
  4. 4. N = 165
  5. 5. P = 0.04636
  6. 6. E(G) = 8 €

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