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

The table gives the probability distribution of X, but one probability is missing. Find P(X = 6).

x: 0, 2, 4, 6p(x): 0.15, 0.3, 0.3, ?

P(X = 6) =

2.Easy

A bag holds 5 red, 6 blue and 4 green balls. You draw one at random. What is the probability P that it is blue?

5 / 6 / 4

P =

3.Medium

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

x: 0, 1, 2, 3p(x): 0.25, 0.35, 0.3, 0.1

Var(X) =

4.Medium

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 =

5.Hard

A game costs €3 to play. You win €15 with probability 0.25 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€15: p = 0.25€30: p = 0.02

E(G) = €

6.Hard

A game costs €10 to play. You win €20 with probability 0.25 and €200 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€20: p = 0.25€200: p = 0.05

E(G) = €

Answer key

1. P(X = 6) = 0.25
2. P = 0.4
3. Var(X) = 0.8875
4. N = 1287
5. E(G) = 1.35 €
6. E(G) = 5 €

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