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
xp(x)00.2510.2520.330.0540.15

A random variable X has the probability distribution shown. Find its expected value E(X).

x: 0, 1, 2, 3, 4p(x): 0.25, 0.25, 0.3, 0.05, 0.15
E(X) =
2.Easy
xp(x)0?10.3520.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 1, 2p(x): ?, 0.35, 0.3
P(X = 0) =
3.Medium
red: 7blue: 8

A bag holds 7 red and 8 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 8
P =
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)−30.8830.1570.02

A game costs €3 to play. You win €6 with probability 0.1 and €60 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€6: p = 0.1€60: p = 0.02
E(G) = €
6.Hard
€p(x)−10.8930.1490.01

A game costs €1 to play. You win €4 with probability 0.1 and €50 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€4: p = 0.1€50: p = 0.01
E(G) = €

Answer key

  1. 1. E(X) = 1.6
  2. 2. P(X = 0) = 0.35
  3. 3. P = 0.2
  4. 4. N = 56
  5. 5. E(G) = −1.2 €
  6. 6. E(G) = −0.1 €

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