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
red: 5blue: 4green: 1

A bag holds 5 red, 4 blue and 1 green balls. You draw one at random. What is the probability P that it is not red?

5 / 4 / 1
P =
2.Easy
xp(x)00.310.3520.35

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
E(X) =
3.Medium
n = 8k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 8? The order does not matter.

n = 8k = 2
N =
4.Medium
xp(x)100.2200.35300.3400.15μ = 24

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

x: 10, 20, 30, 40p(x): 0.2, 0.35, 0.3, 0.15
Var(X) =
5.Hard
n = 11, p = 0.1: P(X = 1) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 1 correct answers?

n = 11p = 0.1k = 1
P =
6.Hard
€p(x)−10.8930.190.01

A game costs €1 to play. You win €4 with probability 0.1 and €10 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€10: p = 0.01
E(G) = €

Answer key

  1. 1. P = 0.5
  2. 2. E(X) = 1.05
  3. 3. N = 28
  4. 4. Var(X) = 94
  5. 5. P = 0.3835
  6. 6. E(G) = −0.5 €

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