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)00.2520.2540.360.2

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

x: 0, 2, 4, 6p(x): 0.25, 0.25, 0.3, 0.2
E(X) =
2.Easy
xp(x)100.220?300.2400.25

The table gives the probability distribution of X, but one probability is missing. Find P(X = 20).

x: 10, 20, 30, 40p(x): 0.2, ?, 0.2, 0.25
P(X = 20) =
3.Medium
P(at least one six) = ??1?2?3P(six) = 1/6 on each roll

A fair die is rolled 3 times. What is the probability P of getting at least one six?

n = 3
P =
4.Medium
xp(x)10.0520.3530.3540.25μ = 2.8

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

x: 1, 2, 3, 4p(x): 0.05, 0.35, 0.35, 0.25
σ =
5.Hard
n = 12, p = 0.4: P(X = 1) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.4, independently. What is the probability P of exactly 1 correct answers?

n = 12p = 0.4k = 1
P =
6.Hard
n = 12, p = 0.5: P(X ≤ 1) = ?k0123456789101112

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

n = 12p = 0.5
P =

Answer key

  1. 1. E(X) = 2.9
  2. 2. P(X = 20) = 0.35
  3. 3. P = 0.4213
  4. 4. σ = 0.8718
  5. 5. P = 0.01741
  6. 6. P = 0.003174

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