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 = 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 11?

2 dice= 11
P =
2.Easy
red: 8blue: 7green: 1

A bag holds 8 red, 7 blue and 1 green balls. You draw one at random. What is the probability P that it is not red?

8 / 7 / 1
P =
3.Medium
xp(x)10.320.1530.2540.150.2μ = 2.75

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.15, 0.25, 0.1, 0.2
Var(X) =
4.Medium
n = 11k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 11? The order does not matter.

n = 11k = 4
N =
5.Hard
xp(x)10.120.3530.1540.250.2μ

X has the distribution shown, and Y = 2X − 3. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.1, 0.35, 0.15, 0.2, 0.2Y = 2X − 3
σY =
6.Hard
xp(x)00.2520.340.1560.3μ

X has the distribution shown, and Y = 2X + 4. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.25, 0.3, 0.15, 0.3Y = 2X + 4
σY =

Answer key

  1. 1. P = 0.05556
  2. 2. P = 0.5
  3. 3. Var(X) = 2.188
  4. 4. N = 330
  5. 5. σY = 2.644
  6. 6. σY = 4.648

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