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: 2blue: 2green: 4

A bag holds 2 red, 2 blue and 4 green balls. You draw one at random. What is the probability P that it is blue?

2 / 2 / 4
P =
2.Easy
xp(x)10.2520.330.240.25

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

x: 1, 2, 3, 4p(x): 0.25, 0.3, 0.2, 0.25
E(X) =
3.Medium
xp(x)100.3200.25300.35400.1μ = 22.5

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

x: 10, 20, 30, 40p(x): 0.3, 0.25, 0.35, 0.1
Var(X) =
4.Medium
n = 9k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 9? The order does not matter.

n = 9k = 5
N =
5.Hard
€p(x)−50.7550.2450.05

A game costs €5 to play. You win €10 with probability 0.2 and €50 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€10: p = 0.2€50: p = 0.05
E(G) = €
6.Hard
n = 9, p = 0.1: P(X = 4) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 4 correct answers?

n = 9p = 0.1k = 4
P =

Answer key

  1. 1. P = 0.25
  2. 2. E(X) = 2.45
  3. 3. Var(X) = 98.75
  4. 4. N = 126
  5. 5. E(G) = −0.5 €
  6. 6. P = 0.00744

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