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: 6blue: 2green: 3

A bag holds 6 red, 2 blue and 3 green balls. You draw one at random. What is the probability P that it is red?

6 / 2 / 3
P =
2.Easy
xp(x)10.12?30.1540.350.25

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 1, 2, 3, 4, 5p(x): 0.1, ?, 0.15, 0.3, 0.25
P(X = 2) =
3.Medium
xp(x)00.3510.0520.1530.140.35μ = 2.05

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

x: 0, 1, 2, 3, 4p(x): 0.35, 0.05, 0.15, 0.1, 0.35
Var(X) =
4.Medium
n = 13k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 13? The order does not matter.

n = 13k = 2
N =
5.Hard
n = 6, p = 0.3: P(X = 2) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 2 correct answers?

n = 6p = 0.3k = 2
P =
6.Hard
n = 10, p = 0.5: P(X = 4) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 4 correct answers?

n = 10p = 0.5k = 4
P =

Answer key

  1. 1. P = 0.5455
  2. 2. P(X = 2) = 0.2
  3. 3. Var(X) = 2.947
  4. 4. N = 78
  5. 5. P = 0.3241
  6. 6. P = 0.2051

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