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

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

x: 0, 2, 4, 6p(x): 0.05, 0.25, 0.35, 0.35

E(X) =

2.Easy

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 0, 1, 2, 3p(x): 0.15, 0.35, 0.15, ?

P(X = 3) =

3.Medium

In how many ways N can a committee of 2 people be chosen from a group of 10? The order does not matter.

n = 10k = 2

N =

4.Medium

A bag holds 7 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 9

P =

5.Hard

X has the distribution shown, and Y = −2X + 1. Find the standard deviation σ_Y of Y.

x: 10, 20, 30, 40p(x): 0.15, 0.25, 0.3, 0.3Y = −2X + 1

σ_Y =

6.Hard

A game costs €5 to play. You win €20 with probability 0.15 and €250 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€20: p = 0.15€250: p = 0.02

E(G) = €

Answer key

1. E(X) = 4
2. P(X = 3) = 0.35
3. N = 45
4. P = 0.175
5. σ_Y = 20.86
6. E(G) = 3 €

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