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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
sum ≥ 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice≥ 4
P =
2.Easy
red: 7blue: 2green: 2

A bag holds 7 red, 2 blue and 2 green balls. You draw one at random. What is the probability P that it is red?

7 / 2 / 2
P =
3.Medium
xp(x)00.110.220.230.340.2μ = 2.3

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

x: 0, 1, 2, 3, 4p(x): 0.1, 0.2, 0.2, 0.3, 0.2
Var(X) =
4.Medium
n = 14k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 14? The order does not matter.

n = 14k = 3
N =
5.Hard
xp(x)00.3510.3520.3μ

X has the distribution shown, and Y = 5X + 20. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.35, 0.3Y = 5X + 20
σY =
6.Hard
€p(x)−20.7560.2980.05

A game costs €2 to play. You win €8 with probability 0.2 and €100 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€8: p = 0.2€100: p = 0.05
E(G) = €

Answer key

  1. 1. P = 0.9167
  2. 2. P = 0.6364
  3. 3. Var(X) = 1.61
  4. 4. N = 364
  5. 5. σY = 4.023
  6. 6. E(G) = 4.6 €

Full step-by-step solutions: practise this topic on examproblems.com.