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: 5blue: 4

A bag holds 5 red and 4 blue balls. You draw one at random. What is the probability P that it is blue?

5 / 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)00.3520.240.3560.1μ = 2.4

For the distribution shown, find the standard deviation σ of X.

x: 0, 2, 4, 6p(x): 0.35, 0.2, 0.35, 0.1
σ =
4.Medium
red: 5blue: 7

A bag holds 5 red and 7 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

5 / 7
P =
5.Hard
n = 5, p = 0.7: P(X = 2) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 2 correct answers?

n = 5p = 0.7k = 2
P =
6.Hard
€p(x)−10.6920.3190.01

A game costs €1 to play. You win €3 with probability 0.3 and €20 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€3: p = 0.3€20: p = 0.01
E(G) = €

Answer key

  1. 1. P = 0.4444
  2. 2. P = 0.1111
  3. 3. σ = 2.059
  4. 4. P = 0.1515
  5. 5. P = 0.1323
  6. 6. E(G) = 0.1 €

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