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)100.35200.25300.1400.3

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

x: 10, 20, 30, 40p(x): 0.35, 0.25, 0.1, 0.3
E(X) =
2.Easy
red: 8blue: 8green: 1

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

8 / 8 / 1
P =
3.Medium
P(at least one six) = ??1?2?3?4?5?6?7P(six) = 1/6 on each roll

A fair die is rolled 7 times. What is the probability P of getting at least one six?

n = 7
P =
4.Medium
xp(x)100.25200.35300.35400.05μ = 22

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

x: 10, 20, 30, 40p(x): 0.25, 0.35, 0.35, 0.05
σ =
5.Hard
n = 9, p = 0.5: P(X ≤ 1) = ?k0123456789

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

n = 9p = 0.5
P =
6.Hard
n = 6, p = 0.25: P(X ≤ 1) = ?k0123456

6 components are tested, and each one fails with probability 0.25, independently. What is the probability P that at most one fails?

n = 6p = 0.25
P =

Answer key

  1. 1. E(X) = 23.5
  2. 2. P = 0.5294
  3. 3. P = 0.7209
  4. 4. σ = 8.718
  5. 5. P = 0.01953
  6. 6. P = 0.5339

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