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
sum = 5die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 5?

2 dice= 5
P =
2.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) =
3.Medium
xp(x)10.320.130.2540.350.05μ = 2.7

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.1, 0.25, 0.3, 0.05
σ =
4.Medium
n = 13k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 13? The order does not matter.

n = 13k = 5
N =
5.Hard
€p(x)−100.74100.25900.01

A game costs €10 to play. You win €20 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 = €10€20: p = 0.25€100: p = 0.01
E(G) = €
6.Hard
xp(x)10.1520.1530.1540.2550.3μ

X has the distribution shown, and Y = −2X + 10. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.15, 0.15, 0.15, 0.25, 0.3Y = −2X + 10
σY =

Answer key

  1. 1. P = 0.1111
  2. 2. E(X) = 0.95
  3. 3. σ = 1.308
  4. 4. N = 1287
  5. 5. E(G) = −4 €
  6. 6. σY = 2.857

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