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)10.320.1530.340.25

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

x: 1, 2, 3, 4p(x): 0.3, 0.15, 0.3, 0.25
E(X) =
2.Easy
red: 2blue: 2green: 1

A bag holds 2 red, 2 blue and 1 green balls. You draw one at random. What is the probability P that it is blue?

2 / 2 / 1
P =
3.Medium
n = 10k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 10? The order does not matter.

n = 10k = 5
N =
4.Medium
xp(x)10.3520.330.240.15μ = 2.15

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

x: 1, 2, 3, 4p(x): 0.35, 0.3, 0.2, 0.15
σ =
5.Hard
n = 7, p = 0.25: P(X = 5) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 5 correct answers?

n = 7p = 0.25k = 5
P =
6.Hard
n = 5, p = 0.25: P(X = 2) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 2 correct answers?

n = 5p = 0.25k = 2
P =

Answer key

  1. 1. E(X) = 2.5
  2. 2. P = 0.4
  3. 3. N = 252
  4. 4. σ = 1.062
  5. 5. P = 0.01154
  6. 6. P = 0.2637

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