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: 5blue: 7green: 2

A bag holds 5 red, 7 blue and 2 green balls. You draw one at random. What is the probability P that it is not red?

5 / 7 / 2
P =
2.Easy
xp(x)10.220.3530.340.15

A random variable X has the probability distribution shown. Find its expected value E(X).

x: 1, 2, 3, 4p(x): 0.2, 0.35, 0.3, 0.15
E(X) =
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
xp(x)00.0520.3540.3560.25μ = 3.6

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

x: 0, 2, 4, 6p(x): 0.05, 0.35, 0.35, 0.25
Var(X) =
5.Hard
xp(x)00.2510.1520.2530.340.05μ

X has the distribution shown, and Y = −2X + 10. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.25, 0.15, 0.25, 0.3, 0.05Y = −2X + 10
σY =
6.Hard
n = 9, p = 0.1: P(X = 3) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 3 correct answers?

n = 9p = 0.1k = 3
P =

Answer key

  1. 1. P = 0.6429
  2. 2. E(X) = 2.4
  3. 3. P = 0.1818
  4. 4. Var(X) = 3.04
  5. 5. σY = 2.52
  6. 6. P = 0.04464

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