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
sum ≥ 3die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 3?

2 dice≥ 3
P =
2.Easy
red: 7blue: 5green: 5

A bag holds 7 red, 5 blue and 5 green balls. You draw one at random. What is the probability P that it is red?

7 / 5 / 5
P =
3.Medium
xp(x)00.3510.320.35μ = 1

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
σ =
4.Medium
red: 5blue: 6

A bag holds 5 red and 6 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

5 / 6
P =
5.Hard
€p(x)−50.68100.32450.02

A game costs €5 to play. You win €15 with probability 0.3 and €250 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€15: p = 0.3€250: p = 0.02
E(G) = €
6.Hard
n = 5, p = 0.2: P(X = 3) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 3 correct answers?

n = 5p = 0.2k = 3
P =

Answer key

  1. 1. P = 0.9722
  2. 2. P = 0.4118
  3. 3. σ = 0.8367
  4. 4. P = 0.1818
  5. 5. E(G) = 4.5 €
  6. 6. P = 0.0512

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