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: 3blue: 5green: 2

A bag holds 3 red, 5 blue and 2 green balls. You draw one at random. What is the probability P that it is blue?

3 / 5 / 2
P =
2.Easy
red: 3blue: 4green: 3

A bag holds 3 red, 4 blue and 3 green balls. You draw one at random. What is the probability P that it is not red?

3 / 4 / 3
P =
3.Medium
n = 8k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 8? The order does not matter.

n = 8k = 5
N =
4.Medium
xp(x)00.0510.320.3530.3μ = 1.9

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

x: 0, 1, 2, 3p(x): 0.05, 0.3, 0.35, 0.3
Var(X) =
5.Hard
€p(x)−50.83100.152450.02

A game costs €5 to play. You win €15 with probability 0.15 and €250 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€15: p = 0.15€250: p = 0.02
E(G) = €
6.Hard
xp(x)00.310.320.1530.25μ

X has the distribution shown, and Y = 3X + 10. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.3, 0.3, 0.15, 0.25Y = 3X + 10
σY =

Answer key

  1. 1. P = 0.5
  2. 2. P = 0.7
  3. 3. N = 56
  4. 4. Var(X) = 0.79
  5. 5. E(G) = 2.25 €
  6. 6. σY = 3.457

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