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
red: 4blue: 6green: 4

A bag holds 4 red, 6 blue and 4 green balls. You draw one at random. What is the probability P that it is not red?

4 / 6 / 4
P =
2.Easy
red: 8blue: 5green: 3

A bag holds 8 red, 5 blue and 3 green balls. You draw one at random. What is the probability P that it is red?

8 / 5 / 3
P =
3.Medium
P(at least one six) = ??1?2?3?4?5?6?7P(six) = 1/6 on each roll

A fair die is rolled 7 times. What is the probability P of getting at least one six?

n = 7
P =
4.Medium
P(at least one six) = ??1?2P(six) = 1/6 on each roll

A fair die is rolled 2 times. What is the probability P of getting at least one six?

n = 2
P =
5.Hard
€p(x)−50.6950.32450.01

A game costs €5 to play. You win €10 with probability 0.3 and €250 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€10: p = 0.3€250: p = 0.01
E(G) = €
6.Hard
xp(x)10.220.3530.2540.2μ

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

x: 1, 2, 3, 4p(x): 0.2, 0.35, 0.25, 0.2Y = 3X − 3
σY =

Answer key

  1. 1. P = 0.7143
  2. 2. P = 0.5
  3. 3. P = 0.7209
  4. 4. P = 0.3056
  5. 5. E(G) = 0.5 €
  6. 6. σY = 3.07

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