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)00.210.1520.353?40.2

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 0, 1, 2, 3, 4p(x): 0.2, 0.15, 0.35, ?, 0.2
P(X = 3) =
2.Easy
xp(x)100.15200.35300.2400.3

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

x: 10, 20, 30, 40p(x): 0.15, 0.35, 0.2, 0.3
E(X) =
3.Medium
xp(x)00.1510.0520.1530.340.35μ = 2.65

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

x: 0, 1, 2, 3, 4p(x): 0.15, 0.05, 0.15, 0.3, 0.35
σ =
4.Medium
xp(x)00.310.3520.35μ = 1.05

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
Var(X) =
5.Hard
xp(x)100.25200.3300.1400.35μ

X has the distribution shown, and Y = 3X + 4. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.25, 0.3, 0.1, 0.35Y = 3X + 4
σY =
6.Hard
xp(x)00.210.2520.2530.3μ

X has the distribution shown, and Y = −2X + 5. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.2, 0.25, 0.25, 0.3Y = −2X + 5
σY =

Answer key

  1. 1. P(X = 3) = 0.1
  2. 2. E(X) = 26.5
  3. 3. σ = 1.388
  4. 4. Var(X) = 0.6475
  5. 5. σY = 36.09
  6. 6. σY = 2.216

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