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: 6

A bag holds 5 red and 6 blue balls. You draw one at random. What is the probability P that it is blue?

5 / 6
P =
2.Easy
red: 5blue: 8green: 2

A bag holds 5 red, 8 blue and 2 green balls. You draw one at random. What is the probability P that it is not red?

5 / 8 / 2
P =
3.Medium
xp(x)00.2510.1520.130.3540.15μ = 2

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

x: 0, 1, 2, 3, 4p(x): 0.25, 0.15, 0.1, 0.35, 0.15
Var(X) =
4.Medium
n = 8k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 8? The order does not matter.

n = 8k = 5
N =
5.Hard
€p(x)−30.6860.3270.02

A game costs €3 to play. You win €9 with probability 0.3 and €30 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€9: p = 0.3€30: p = 0.02
E(G) = €
6.Hard
n = 8, p = 0.7: P(X = 3) = ?k012345678

A test has 8 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 3 correct answers?

n = 8p = 0.7k = 3
P =

Answer key

  1. 1. P = 0.5455
  2. 2. P = 0.6667
  3. 3. Var(X) = 2.1
  4. 4. N = 56
  5. 5. E(G) = 0.3 €
  6. 6. P = 0.04668

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