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)100.1200.35300.25400.3

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

x: 10, 20, 30, 40p(x): 0.1, 0.35, 0.25, 0.3
E(X) =
2.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 =
3.Medium
xp(x)00.120.240.3560.35μ = 3.9

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

x: 0, 2, 4, 6p(x): 0.1, 0.2, 0.35, 0.35
σ =
4.Medium
xp(x)00.3510.0520.0530.340.25μ = 2.05

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

x: 0, 1, 2, 3, 4p(x): 0.35, 0.05, 0.05, 0.3, 0.25
Var(X) =
5.Hard
xp(x)10.2520.230.140.1550.3μ

X has the distribution shown, and Y = 0.5X + 4. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.25, 0.2, 0.1, 0.15, 0.3Y = 0.5X + 4
σY =
6.Hard
xp(x)00.0510.1520.3530.2540.2μ

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

x: 0, 1, 2, 3, 4p(x): 0.05, 0.15, 0.35, 0.25, 0.2Y = 2X + 5
σY =

Answer key

  1. 1. E(X) = 27.5
  2. 2. P = 0.7222
  3. 3. σ = 1.947
  4. 4. Var(X) = 2.747
  5. 5. σY = 0.798
  6. 6. σY = 2.227

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