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)10.2520.2530.140.3550.05

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

x: 1, 2, 3, 4, 5p(x): 0.25, 0.25, 0.1, 0.35, 0.05
E(X) =
2.Easy
xp(x)10.3520.330.240.055?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 5).

x: 1, 2, 3, 4, 5p(x): 0.35, 0.3, 0.2, 0.05, ?
P(X = 5) =
3.Medium
xp(x)10.2520.330.1540.0550.25μ = 2.75

For the distribution shown, find the variance Var(X) of X.

x: 1, 2, 3, 4, 5p(x): 0.25, 0.3, 0.15, 0.05, 0.25
Var(X) =
4.Medium
n = 12k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 12? The order does not matter.

n = 12k = 5
N =
5.Hard
xp(x)00.3510.120.330.25μ

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

x: 0, 1, 2, 3p(x): 0.35, 0.1, 0.3, 0.25Y = −2X + 5
σY =
6.Hard
n = 9, p = 0.2: P(X ≤ 1) = ?k0123456789

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

n = 9p = 0.2
P =

Answer key

  1. 1. E(X) = 2.7
  2. 2. P(X = 5) = 0.1
  3. 3. Var(X) = 2.287
  4. 4. N = 792
  5. 5. σY = 2.406
  6. 6. P = 0.4362

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