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
red: 7blue: 8green: 4

A bag holds 7 red, 8 blue and 4 green balls. You draw one at random. What is the probability P that it is blue?

7 / 8 / 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
red: 5blue: 6

A bag holds 5 red and 6 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

5 / 6
P =
4.Medium
n = 15k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 15? The order does not matter.

n = 15k = 3
N =
5.Hard
€p(x)−30.7390.251470.02

A game costs €3 to play. You win €12 with probability 0.25 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€12: p = 0.25€150: p = 0.02
E(G) = €
6.Hard
xp(x)10.320.230.240.2550.05μ

X has the distribution shown, and Y = 0.5X + 10. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.3, 0.2, 0.2, 0.25, 0.05Y = 0.5X + 10
σY =

Answer key

  1. 1. P = 0.4211
  2. 2. P = 0.1389
  3. 3. P = 0.1818
  4. 4. N = 455
  5. 5. E(G) = 3 €
  6. 6. σY = 0.6418

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