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)100.25200.25300.35400.15

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

x: 10, 20, 30, 40p(x): 0.25, 0.25, 0.35, 0.15
E(X) =
2.Easy
red: 2blue: 3green: 1

A bag holds 2 red, 3 blue and 1 green balls. You draw one at random. What is the probability P that it is red?

2 / 3 / 1
P =
3.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 =
4.Medium
xp(x)100.05200.35300.35400.25μ = 28

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

x: 10, 20, 30, 40p(x): 0.05, 0.35, 0.35, 0.25
σ =
5.Hard
n = 9, p = 0.6: P(X ≤ 1) = ?k0123456789

9 components are tested, and each one fails with probability 0.6, independently. What is the probability P that at most one fails?

n = 9p = 0.6
P =
6.Hard
n = 7, p = 0.2: P(X ≤ 1) = ?k01234567

7 components are tested, and each one fails with probability 0.2, independently. What is the probability P that at most one fails?

n = 7p = 0.2
P =

Answer key

  1. 1. E(X) = 24
  2. 2. P = 0.3333
  3. 3. N = 21
  4. 4. σ = 8.718
  5. 5. P = 0.003801
  6. 6. P = 0.5767

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