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)10.3520.1530.240.3

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

x: 1, 2, 3, 4p(x): 0.35, 0.15, 0.2, 0.3
E(X) =
2.Easy
xp(x)100.3200.2300.3540?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 40).

x: 10, 20, 30, 40p(x): 0.3, 0.2, 0.35, ?
P(X = 40) =
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
n = 9k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 9? The order does not matter.

n = 9k = 5
N =
5.Hard
€p(x)−30.7360.251470.02

A game costs €3 to play. You win €9 with probability 0.25 and €150 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€9: p = 0.25€150: p = 0.02
E(G) = €
6.Hard
n = 12, p = 0.7: P(X ≤ 1) = ?k0123456789101112

12 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 12p = 0.7
P =

Answer key

  1. 1. E(X) = 2.45
  2. 2. P(X = 40) = 0.15
  3. 3. P = 0.4213
  4. 4. N = 126
  5. 5. E(G) = 2.25 €
  6. 6. P = 1.541 × 10⁻⁵

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