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: 3green: 2

A bag holds 5 red, 3 blue and 2 green balls. You draw one at random. What is the probability P that it is not red?

5 / 3 / 2
P =
2.Easy
xp(x)10.2520.2530.240.055?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 5).

x: 1, 2, 3, 4, 5p(x): 0.25, 0.25, 0.2, 0.05, ?
P(X = 5) =
3.Medium
red: 6blue: 4

A bag holds 6 red and 4 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

6 / 4
P =
4.Medium
xp(x)00.3510.220.230.25μ = 1.35

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

x: 0, 1, 2, 3p(x): 0.35, 0.2, 0.2, 0.25
σ =
5.Hard
€p(x)−10.6910.3190.01

A game costs €1 to play. You win €2 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€2: p = 0.3€20: p = 0.01
E(G) = €
6.Hard
n = 9, p = 0.5: P(X ≤ 1) = ?k0123456789

9 components are tested, and each one fails with probability 0.5, independently. What is the probability P that at most one fails?

n = 9p = 0.5
P =

Answer key

  1. 1. P = 0.5
  2. 2. P(X = 5) = 0.25
  3. 3. P = 0.3333
  4. 4. σ = 1.195
  5. 5. E(G) = −0.2 €
  6. 6. P = 0.01953

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