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
xp(x)00.3520.2540.260.2

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

x: 0, 2, 4, 6p(x): 0.35, 0.25, 0.2, 0.2
E(X) =
2.Easy
red: 8blue: 8green: 1

A bag holds 8 red, 8 blue and 1 green balls. You draw one at random. What is the probability P that it is red?

8 / 8 / 1
P =
3.Medium
xp(x)10.0520.230.2540.3550.15μ = 3.35

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

x: 1, 2, 3, 4, 5p(x): 0.05, 0.2, 0.25, 0.35, 0.15
Var(X) =
4.Medium
n = 12k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 12? The order does not matter.

n = 12k = 4
N =
5.Hard
n = 11, p = 0.4: P(X = 1) = ?k01234567891011

A test has 11 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 = 11p = 0.4k = 1
P =
6.Hard
€p(x)−30.8930.1570.01

A game costs €3 to play. You win €6 with probability 0.1 and €60 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€6: p = 0.1€60: p = 0.01
E(G) = €

Answer key

  1. 1. E(X) = 2.5
  2. 2. P = 0.4706
  3. 3. Var(X) = 1.228
  4. 4. N = 495
  5. 5. P = 0.02661
  6. 6. E(G) = −1.8 €

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