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)00.0510.3520.130.2540.25

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

x: 0, 1, 2, 3, 4p(x): 0.05, 0.35, 0.1, 0.25, 0.25
E(X) =
2.Easy
red: 4blue: 3green: 3

A bag holds 4 red, 3 blue and 3 green balls. You draw one at random. What is the probability P that it is red?

4 / 3 / 3
P =
3.Medium
xp(x)00.310.3520.35μ = 1.05

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
Var(X) =
4.Medium
n = 15k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 15? The order does not matter.

n = 15k = 4
N =
5.Hard
xp(x)100.1200.35300.3400.25μ

X has the distribution shown, and Y = 3X + 20. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.1, 0.35, 0.3, 0.25Y = 3X + 20
σY =
6.Hard
€p(x)−10.7540.290.05

A game costs €1 to play. You win €5 with probability 0.2 and €10 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€5: p = 0.2€10: p = 0.05
E(G) = €

Answer key

  1. 1. E(X) = 2.3
  2. 2. P = 0.4
  3. 3. Var(X) = 0.6475
  4. 4. N = 1365
  5. 5. σY = 28.62
  6. 6. E(G) = 0.5 €

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