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)10.120.330.340.2550.05

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

x: 1, 2, 3, 4, 5p(x): 0.1, 0.3, 0.3, 0.25, 0.05
E(X) =
2.Easy
sum ≥ 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 11?

2 dice≥ 11
P =
3.Medium
xp(x)100.15200.3300.3400.25μ = 26.5

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

x: 10, 20, 30, 40p(x): 0.15, 0.3, 0.3, 0.25
Var(X) =
4.Medium
n = 8k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 8? The order does not matter.

n = 8k = 2
N =
5.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = −2X + 4. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = −2X + 4
σY =
6.Hard
xp(x)00.310.1520.1530.240.2μ

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

x: 0, 1, 2, 3, 4p(x): 0.3, 0.15, 0.15, 0.2, 0.2Y = −2X + 5
σY =

Answer key

  1. 1. E(X) = 2.85
  2. 2. P = 0.08333
  3. 3. Var(X) = 102.8
  4. 4. N = 28
  5. 5. σY = 1.673
  6. 6. σY = 3.051

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