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: 4blue: 6green: 3

A bag holds 4 red, 6 blue and 3 green balls. You draw one at random. What is the probability P that it is blue?

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

A bag holds 5 red, 2 blue and 4 green balls. You draw one at random. What is the probability P that it is blue?

5 / 2 / 4
P =
3.Medium
xp(x)100.2200.3300.35400.15μ = 24.5

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

x: 10, 20, 30, 40p(x): 0.2, 0.3, 0.35, 0.15
Var(X) =
4.Medium
red: 8blue: 3

A bag holds 8 red and 3 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

8 / 3
P =
5.Hard
n = 5, p = 0.3: P(X = 3) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 3 correct answers?

n = 5p = 0.3k = 3
P =
6.Hard
€p(x)−30.7460.25270.01

A game costs €3 to play. You win €9 with probability 0.25 and €30 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€9: p = 0.25€30: p = 0.01
E(G) = €

Answer key

  1. 1. P = 0.4615
  2. 2. P = 0.1818
  3. 3. Var(X) = 94.75
  4. 4. P = 0.5091
  5. 5. P = 0.1323
  6. 6. E(G) = −0.45 €

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