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: 6blue: 7green: 4

A bag holds 6 red, 7 blue and 4 green balls. You draw one at random. What is the probability P that it is red?

6 / 7 / 4
P =
2.Easy
sum = 5die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 5?

2 dice= 5
P =
3.Medium
xp(x)00.2520.240.360.25μ = 3.1

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

x: 0, 2, 4, 6p(x): 0.25, 0.2, 0.3, 0.25
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4?5P(six) = 1/6 on each roll

A fair die is rolled 5 times. What is the probability P of getting at least one six?

n = 5
P =
5.Hard
€p(x)−50.8450.15450.01

A game costs €5 to play. You win €10 with probability 0.15 and €50 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 = 0.15€50: p = 0.01
E(G) = €
6.Hard
n = 10, p = 0.6: P(X ≤ 1) = ?k012345678910

10 components are tested, and each one fails with probability 0.6, independently. What is the probability P that at most one fails?

n = 10p = 0.6
P =

Answer key

  1. 1. P = 0.3529
  2. 2. P = 0.1111
  3. 3. Var(X) = 4.99
  4. 4. P = 0.5981
  5. 5. E(G) = −3 €
  6. 6. P = 0.001678

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