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: 4blue: 2

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

4 / 2
P =
2.Easy
xp(x)00.210.3520.1530.3

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

x: 0, 1, 2, 3p(x): 0.2, 0.35, 0.15, 0.3
E(X) =
3.Medium
n = 7k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 7? The order does not matter.

n = 7k = 2
N =
4.Medium
P(at least one six) = ??1?2?3?4?5?6?7P(six) = 1/6 on each roll

A fair die is rolled 7 times. What is the probability P of getting at least one six?

n = 7
P =
5.Hard
€p(x)−20.7480.25980.01

A game costs €2 to play. You win €10 with probability 0.25 and €100 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€10: p = 0.25€100: p = 0.01
E(G) = €
6.Hard
n = 7, p = 0.25: P(X = 1) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 1 correct answers?

n = 7p = 0.25k = 1
P =

Answer key

  1. 1. P = 0.6667
  2. 2. E(X) = 1.55
  3. 3. N = 21
  4. 4. P = 0.7209
  5. 5. E(G) = 1.5 €
  6. 6. P = 0.3115

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