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 = 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 4?

2 dice= 4
P =
2.Easy
sum = 8die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 8?

2 dice= 8
P =
3.Medium
n = 10k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 10? The order does not matter.

n = 10k = 4
N =
4.Medium
xp(x)100.3200.2300.15400.35μ = 25.5

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

x: 10, 20, 30, 40p(x): 0.3, 0.2, 0.15, 0.35
σ =
5.Hard
€p(x)−30.6830.31470.02

A game costs €3 to play. You win €6 with probability 0.3 and €150 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€6: p = 0.3€150: p = 0.02
E(G) = €
6.Hard
n = 5, p = 0.7: P(X ≤ 1) = ?k012345

5 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 5p = 0.7
P =

Answer key

  1. 1. P = 0.08333
  2. 2. P = 0.1389
  3. 3. N = 210
  4. 4. σ = 12.44
  5. 5. E(G) = 1.8 €
  6. 6. P = 0.03078

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