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)0?10.320.35

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

x: 0, 1, 2p(x): ?, 0.3, 0.35
P(X = 0) =
2.Easy
red: 6blue: 7green: 2

A bag holds 6 red, 7 blue and 2 green balls. You draw one at random. What is the probability P that it is red?

6 / 7 / 2
P =
3.Medium
n = 13k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 13? The order does not matter.

n = 13k = 5
N =
4.Medium
xp(x)10.2520.130.140.3550.2μ = 3.15

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

x: 1, 2, 3, 4, 5p(x): 0.25, 0.1, 0.1, 0.35, 0.2
Var(X) =
5.Hard
€p(x)−20.7580.2380.05

A game costs €2 to play. You win €10 with probability 0.2 and €40 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€10: p = 0.2€40: p = 0.05
E(G) = €
6.Hard
€p(x)−100.73200.25900.02

A game costs €10 to play. You win €30 with probability 0.25 and €100 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€30: p = 0.25€100: p = 0.02
E(G) = €

Answer key

  1. 1. P(X = 0) = 0.35
  2. 2. P = 0.4
  3. 3. N = 1287
  4. 4. Var(X) = 2.227
  5. 5. E(G) = 2 €
  6. 6. E(G) = −0.5 €

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