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)10.0520.2530.3540.250.15

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

x: 1, 2, 3, 4, 5p(x): 0.05, 0.25, 0.35, 0.2, 0.15
E(X) =
2.Easy
sum = 5die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 5?

2 dice= 5
P =
3.Medium
xp(x)00.3520.140.3560.2μ = 2.8

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

x: 0, 2, 4, 6p(x): 0.35, 0.1, 0.35, 0.2
σ =
4.Medium
xp(x)10.1520.230.340.35μ = 2.85

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

x: 1, 2, 3, 4p(x): 0.15, 0.2, 0.3, 0.35
Var(X) =
5.Hard
xp(x)00.310.3520.35μ

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

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

9 components are tested, and each one fails with probability 0.25, independently. What is the probability P that at most one fails?

n = 9p = 0.25
P =

Answer key

  1. 1. E(X) = 3.15
  2. 2. P = 0.1111
  3. 3. σ = 2.315
  4. 4. Var(X) = 1.128
  5. 5. σY = 1.609
  6. 6. P = 0.3003

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