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)10.3520.0530.340.3

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

x: 1, 2, 3, 4p(x): 0.35, 0.05, 0.3, 0.3
E(X) =
2.Easy
xp(x)10.2520.33?40.15

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

x: 1, 2, 3, 4p(x): 0.25, 0.3, ?, 0.15
P(X = 3) =
3.Medium
n = 11k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 11? The order does not matter.

n = 11k = 4
N =
4.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 =
5.Hard
xp(x)10.2520.330.240.0550.2μ

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

x: 1, 2, 3, 4, 5p(x): 0.25, 0.3, 0.2, 0.05, 0.2Y = 3X + 4
σY =
6.Hard
n = 8, p = 0.2: P(X ≤ 1) = ?k012345678

8 components are tested, and each one fails with probability 0.2, independently. What is the probability P that at most one fails?

n = 8p = 0.2
P =

Answer key

  1. 1. E(X) = 2.55
  2. 2. P(X = 3) = 0.3
  3. 3. N = 330
  4. 4. P = 0.5177
  5. 5. σY = 4.272
  6. 6. P = 0.5033

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