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.

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Name: ____________________   Date: ____________

1.Easy
red: 8blue: 5green: 2

A bag holds 8 red, 5 blue and 2 green balls. You draw one at random. What is the probability P that it is blue?

8 / 5 / 2
P =
2.Easy
sum = 8die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 8?

2 dice= 8
P =
3.Medium
xp(x)00.1510.2520.3530.140.15μ = 1.85

For the distribution shown, find the variance Var(X) of X.

x: 0, 1, 2, 3, 4p(x): 0.15, 0.25, 0.35, 0.1, 0.15
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4?5?6?7?8P(six) = 1/6 on each roll

A fair die is rolled 8 times. What is the probability P of getting at least one six?

n = 8
P =
5.Hard
€p(x)−20.7360.25380.02

A game costs €2 to play. You win €8 with probability 0.25 and €40 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€8: p = 0.25€40: p = 0.02
E(G) = €
6.Hard
n = 11, p = 0.6: P(X = 2) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.6, independently. What is the probability P of exactly 2 correct answers?

n = 11p = 0.6k = 2
P =

Answer key

  1. 1. P = 0.3333
  2. 2. P = 0.1389
  3. 3. Var(X) = 1.527
  4. 4. P = 0.7674
  5. 5. E(G) = 0.8 €
  6. 6. P = 0.00519

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