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: 8blue: 2green: 5

A bag holds 8 red, 2 blue and 5 green balls. You draw one at random. What is the probability P that it is not red?

8 / 2 / 5
P =
2.Easy
xp(x)00.3520.14?60.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 4).

x: 0, 2, 4, 6p(x): 0.35, 0.1, ?, 0.35
P(X = 4) =
3.Medium
xp(x)10.120.1530.340.150.35μ = 3.45

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

x: 1, 2, 3, 4, 5p(x): 0.1, 0.15, 0.3, 0.1, 0.35
Var(X) =
4.Medium
red: 3blue: 9

A bag holds 3 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 9
P =
5.Hard
n = 12, p = 0.25: P(X ≤ 1) = ?k0123456789101112

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

n = 12p = 0.25
P =
6.Hard
xp(x)10.220.2530.1540.150.3μ

X has the distribution shown, and Y = 5X + 1. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.2, 0.25, 0.15, 0.1, 0.3Y = 5X + 1
σY =

Answer key

  1. 1. P = 0.4667
  2. 2. P(X = 4) = 0.2
  3. 3. Var(X) = 1.848
  4. 4. P = 0.04545
  5. 5. P = 0.1584
  6. 6. σY = 7.661

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