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
sum ≥ 6die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 6?

2 dice≥ 6
P =
2.Easy
xp(x)00.2510.3520.230.2

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

x: 0, 1, 2, 3p(x): 0.25, 0.35, 0.2, 0.2
E(X) =
3.Medium
xp(x)00.3510.320.35μ = 1

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
Var(X) =
4.Medium
n = 12k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 12? The order does not matter.

n = 12k = 4
N =
5.Hard
xp(x)00.1520.3540.1560.35μ

X has the distribution shown, and Y = 5X + 20. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.15, 0.35, 0.15, 0.35Y = 5X + 20
σY =
6.Hard
xp(x)100.35200.15300.3400.2μ

X has the distribution shown, and Y = 10X + 5. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.35, 0.15, 0.3, 0.2Y = 10X + 5
σY =

Answer key

  1. 1. P = 0.7222
  2. 2. E(X) = 1.35
  3. 3. Var(X) = 0.7
  4. 4. N = 495
  5. 5. σY = 11
  6. 6. σY = 115.2

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