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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1.Easy
xp(x)00.3520.240.3560.1

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

x: 0, 2, 4, 6p(x): 0.35, 0.2, 0.35, 0.1
E(X) =
2.Easy
red: 2blue: 3green: 3

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

2 / 3 / 3
P =
3.Medium
xp(x)10.3520.0530.3540.25μ = 2.5

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

x: 1, 2, 3, 4p(x): 0.35, 0.05, 0.35, 0.25
σ =
4.Medium
n = 7k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 7? The order does not matter.

n = 7k = 5
N =
5.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = 3X + 5. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = 3X + 5
σY =
6.Hard
n = 11, p = 0.2: P(X = 4) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 4 correct answers?

n = 11p = 0.2k = 4
P =

Answer key

  1. 1. E(X) = 2.4
  2. 2. P = 0.25
  3. 3. σ = 1.204
  4. 4. N = 21
  5. 5. σY = 2.51
  6. 6. P = 0.1107

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