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)10.320.130.240.250.2

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.1, 0.2, 0.2, 0.2
E(X) =
2.Easy
xp(x)100.120?300.3400.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 20).

x: 10, 20, 30, 40p(x): 0.1, ?, 0.3, 0.3
P(X = 20) =
3.Medium
xp(x)10.2520.3530.340.1μ = 2.25

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

x: 1, 2, 3, 4p(x): 0.25, 0.35, 0.3, 0.1
σ =
4.Medium
n = 9k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 9? The order does not matter.

n = 9k = 5
N =
5.Hard
xp(x)100.05200.35300.35400.25μ

X has the distribution shown, and Y = −2X + 1. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.05, 0.35, 0.35, 0.25Y = −2X + 1
σY =
6.Hard
n = 9, p = 0.5: P(X ≤ 1) = ?k0123456789

9 components are tested, and each one fails with probability 0.5, independently. What is the probability P that at most one fails?

n = 9p = 0.5
P =

Answer key

  1. 1. E(X) = 2.9
  2. 2. P(X = 20) = 0.3
  3. 3. σ = 0.9421
  4. 4. N = 126
  5. 5. σY = 17.44
  6. 6. P = 0.01953

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