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 = 6die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 6?

2 dice= 6
P =
2.Easy
red: 3blue: 4

A bag holds 3 red and 4 blue balls. You draw one at random. What is the probability P that it is blue?

3 / 4
P =
3.Medium
xp(x)00.310.0520.2530.1540.25μ = 2

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

x: 0, 1, 2, 3, 4p(x): 0.3, 0.05, 0.25, 0.15, 0.25
Var(X) =
4.Medium
red: 6blue: 8

A bag holds 6 red and 8 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

6 / 8
P =
5.Hard
n = 12, p = 0.7: P(X = 4) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 4 correct answers?

n = 12p = 0.7k = 4
P =
6.Hard
€p(x)−10.6820.390.02

A game costs €1 to play. You win €3 with probability 0.3 and €10 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€3: p = 0.3€10: p = 0.02
E(G) = €

Answer key

  1. 1. P = 0.1389
  2. 2. P = 0.5714
  3. 3. Var(X) = 2.4
  4. 4. P = 0.1648
  5. 5. P = 0.007798
  6. 6. E(G) = 0.1 €

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