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)10.22?30.1540.35

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

x: 1, 2, 3, 4p(x): 0.2, ?, 0.15, 0.35
P(X = 2) =
2.Easy
xp(x)10.0520.3530.3540.25

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

x: 1, 2, 3, 4p(x): 0.05, 0.35, 0.35, 0.25
E(X) =
3.Medium
xp(x)00.3510.220.130.240.15μ = 1.6

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

x: 0, 1, 2, 3, 4p(x): 0.35, 0.2, 0.1, 0.2, 0.15
σ =
4.Medium
n = 15k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 15? The order does not matter.

n = 15k = 5
N =
5.Hard
xp(x)00.110.2520.1530.1540.35μ

X has the distribution shown, and Y = 2X + 5. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.1, 0.25, 0.15, 0.15, 0.35Y = 2X + 5
σY =
6.Hard
n = 9, p = 0.7: P(X ≤ 1) = ?k0123456789

9 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 9p = 0.7
P =

Answer key

  1. 1. P(X = 2) = 0.3
  2. 2. E(X) = 2.8
  3. 3. σ = 1.497
  4. 4. N = 3003
  5. 5. σY = 2.857
  6. 6. P = 0.000433

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