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: 7blue: 6green: 3

A bag holds 7 red, 6 blue and 3 green balls. You draw one at random. What is the probability P that it is not red?

7 / 6 / 3
P =
2.Easy
red: 4blue: 7green: 4

A bag holds 4 red, 7 blue and 4 green balls. You draw one at random. What is the probability P that it is blue?

4 / 7 / 4
P =
3.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
Var(X) =
4.Medium
n = 7k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 7? The order does not matter.

n = 7k = 3
N =
5.Hard
n = 10, p = 0.2: P(X = 5) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 5 correct answers?

n = 10p = 0.2k = 5
P =
6.Hard
xp(x)00.310.0520.230.140.35μ

X has the distribution shown, and Y = −2X + 20. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.3, 0.05, 0.2, 0.1, 0.35Y = −2X + 20
σY =

Answer key

  1. 1. P = 0.5625
  2. 2. P = 0.4667
  3. 3. Var(X) = 0.6475
  4. 4. N = 35
  5. 5. P = 0.02642
  6. 6. σY = 3.303

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