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)00.1510.320.1530.2540.15

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

x: 0, 1, 2, 3, 4p(x): 0.15, 0.3, 0.15, 0.25, 0.15
E(X) =
2.Easy
sum = 9die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 9?

2 dice= 9
P =
3.Medium
P(at least one six) = ??1?2?3?4P(six) = 1/6 on each roll

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
4.Medium
n = 9k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 9? The order does not matter.

n = 9k = 4
N =
5.Hard
n = 12, p = 0.7: P(X = 4) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 4 correct answers?

n = 12p = 0.7k = 4
P =
6.Hard
n = 11, p = 0.25: P(X ≤ 1) = ?k01234567891011

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

n = 11p = 0.25
P =

Answer key

  1. 1. E(X) = 1.95
  2. 2. P = 0.1111
  3. 3. P = 0.5177
  4. 4. N = 126
  5. 5. P = 0.007798
  6. 6. P = 0.1971

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