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)00.320.1540.2560.3

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

x: 0, 2, 4, 6p(x): 0.3, 0.15, 0.25, 0.3
E(X) =
2.Easy
red: 5blue: 5green: 5

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

5 / 5 / 5
P =
3.Medium
xp(x)00.310.0520.3530.3μ = 1.65

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

x: 0, 1, 2, 3p(x): 0.3, 0.05, 0.35, 0.3
σ =
4.Medium
red: 6blue: 9

A bag holds 6 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

6 / 9
P =
5.Hard
xp(x)10.120.330.1540.1550.3μ

X has the distribution shown, and Y = 3X + 1. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.1, 0.3, 0.15, 0.15, 0.3Y = 3X + 1
σY =
6.Hard
n = 7, p = 0.2: P(X ≤ 1) = ?k01234567

7 components are tested, and each one fails with probability 0.2, independently. What is the probability P that at most one fails?

n = 7p = 0.2
P =

Answer key

  1. 1. E(X) = 3.1
  2. 2. P = 0.6667
  3. 3. σ = 1.195
  4. 4. P = 0.1429
  5. 5. σY = 4.229
  6. 6. P = 0.5767

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