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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1.Easy
xp(x)1?20.1530.2540.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 1, 2, 3, 4p(x): ?, 0.15, 0.25, 0.3
P(X = 1) =
2.Easy
red: 8blue: 8green: 4

A bag holds 8 red, 8 blue and 4 green balls. You draw one at random. What is the probability P that it is blue?

8 / 8 / 4
P =
3.Medium
xp(x)00.210.1520.3530.3μ = 1.75

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

x: 0, 1, 2, 3p(x): 0.2, 0.15, 0.35, 0.3
σ =
4.Medium
n = 8k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 8? The order does not matter.

n = 8k = 3
N =
5.Hard
xp(x)10.2520.130.3540.3μ

X has the distribution shown, and Y = −2X + 10. Find the standard deviation σY of Y.

x: 1, 2, 3, 4p(x): 0.25, 0.1, 0.35, 0.3Y = −2X + 10
σY =
6.Hard
€p(x)−20.8460.15380.01

A game costs €2 to play. You win €8 with probability 0.15 and €40 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€8: p = 0.15€40: p = 0.01
E(G) = €

Answer key

  1. 1. P(X = 1) = 0.3
  2. 2. P = 0.4
  3. 3. σ = 1.09
  4. 4. N = 56
  5. 5. σY = 2.289
  6. 6. E(G) = −0.4 €

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