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 = 8die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 8?

2 dice= 8
P =
2.Easy
red: 6blue: 5green: 3

A bag holds 6 red, 5 blue and 3 green balls. You draw one at random. What is the probability P that it is red?

6 / 5 / 3
P =
3.Medium
xp(x)00.2520.3540.160.3μ = 2.9

For the distribution shown, find the standard deviation σ of X.

x: 0, 2, 4, 6p(x): 0.25, 0.35, 0.1, 0.3
σ =
4.Medium
n = 15k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 15? The order does not matter.

n = 15k = 4
N =
5.Hard
n = 5, p = 0.5: P(X = 4) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 4 correct answers?

n = 5p = 0.5k = 4
P =
6.Hard
n = 8, p = 0.5: P(X ≤ 1) = ?k012345678

8 components are tested, and each one fails with probability 0.5, independently. What is the probability P that at most one fails?

n = 8p = 0.5
P =

Answer key

  1. 1. P = 0.1389
  2. 2. P = 0.4286
  3. 3. σ = 2.322
  4. 4. N = 1365
  5. 5. P = 0.1563
  6. 6. P = 0.03516

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