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)100.1200.25300.35400.3

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

x: 10, 20, 30, 40p(x): 0.1, 0.25, 0.35, 0.3
E(X) =
2.Easy
red: 6blue: 8green: 5

A bag holds 6 red, 8 blue and 5 green balls. You draw one at random. What is the probability P that it is red?

6 / 8 / 5
P =
3.Medium
xp(x)100.1200.25300.3400.35μ = 29

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

x: 10, 20, 30, 40p(x): 0.1, 0.25, 0.3, 0.35
σ =
4.Medium
xp(x)00.310.220.3530.15μ = 1.35

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

x: 0, 1, 2, 3p(x): 0.3, 0.2, 0.35, 0.15
Var(X) =
5.Hard
xp(x)00.210.120.3530.2540.1μ

X has the distribution shown, and Y = 3X + 5. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.2, 0.1, 0.35, 0.25, 0.1Y = 3X + 5
σY =
6.Hard
n = 8, p = 0.5: P(X ≤ 1) = ?k012345678

8 components are tested, and each one fails with probability 0.5, independently. What is the probability P that at most one fails?

n = 8p = 0.5
P =

Answer key

  1. 1. E(X) = 28.5
  2. 2. P = 0.3158
  3. 3. σ = 9.95
  4. 4. Var(X) = 1.128
  5. 5. σY = 3.732
  6. 6. P = 0.03516

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