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)00.352?40.2560.2

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 0, 2, 4, 6p(x): 0.35, ?, 0.25, 0.2
P(X = 2) =
2.Easy
xp(x)10.2520.2530.154?

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

x: 1, 2, 3, 4p(x): 0.25, 0.25, 0.15, ?
P(X = 4) =
3.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
Var(X) =
4.Medium
red: 8blue: 5

A bag holds 8 red and 5 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

8 / 5
P =
5.Hard
xp(x)10.320.230.0540.250.25μ

X has the distribution shown, and Y = 5X + 10. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.3, 0.2, 0.05, 0.2, 0.25Y = 5X + 10
σY =
6.Hard
xp(x)00.210.3520.3530.0540.05μ

X has the distribution shown, and Y = −2X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.2, 0.35, 0.35, 0.05, 0.05Y = −2X + 1
σY =

Answer key

  1. 1. P(X = 2) = 0.2
  2. 2. P(X = 4) = 0.35
  3. 3. Var(X) = 0.6475
  4. 4. P = 0.359
  5. 5. σY = 8.047
  6. 6. σY = 2.04

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