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
xp(x)00.110.32?30.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 0, 1, 2, 3p(x): 0.1, 0.3, ?, 0.35
P(X = 2) =
2.Easy
red: 8blue: 6

A bag holds 8 red and 6 blue balls. You draw one at random. What is the probability P that it is blue?

8 / 6
P =
3.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 =
4.Medium
xp(x)100.35200.35300.15400.15μ = 21

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

x: 10, 20, 30, 40p(x): 0.35, 0.35, 0.15, 0.15
Var(X) =
5.Hard
€p(x)−100.8100.15900.05

A game costs €10 to play. You win €20 with probability 0.15 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 = €10€20: p = 0.15€100: p = 0.05
E(G) = €
6.Hard
n = 8, p = 0.7: P(X = 2) = ?k012345678

A test has 8 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 2 correct answers?

n = 8p = 0.7k = 2
P =

Answer key

  1. 1. P(X = 2) = 0.25
  2. 2. P = 0.4286
  3. 3. N = 165
  4. 4. Var(X) = 109
  5. 5. E(G) = −2 €
  6. 6. P = 0.01

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