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
xp(x)00.3510.3520.3

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
E(X) =
2.Easy
red: 2blue: 7green: 3

A bag holds 2 red, 7 blue and 3 green balls. You draw one at random. What is the probability P that it is red?

2 / 7 / 3
P =
3.Medium
n = 12k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 12? The order does not matter.

n = 12k = 3
N =
4.Medium
xp(x)00.110.3520.230.340.05μ = 1.85

For the distribution shown, find the standard deviation σ of X.

x: 0, 1, 2, 3, 4p(x): 0.1, 0.35, 0.2, 0.3, 0.05
σ =
5.Hard
n = 7, p = 0.4: P(X = 1) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.4, independently. What is the probability P of exactly 1 correct answers?

n = 7p = 0.4k = 1
P =
6.Hard
€p(x)−100.89200.14900.01

A game costs €10 to play. You win €30 with probability 0.1 and €500 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€30: p = 0.1€500: p = 0.01
E(G) = €

Answer key

  1. 1. E(X) = 0.95
  2. 2. P = 0.1667
  3. 3. N = 220
  4. 4. σ = 1.108
  5. 5. P = 0.1306
  6. 6. E(G) = −2 €

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