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)00.3510.320.35

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
E(X) =
2.Easy
xp(x)00.351?20.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 0, 1, 2p(x): 0.35, ?, 0.35
P(X = 1) =
3.Medium
xp(x)00.310.3520.230.140.05μ = 1.25

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

x: 0, 1, 2, 3, 4p(x): 0.3, 0.35, 0.2, 0.1, 0.05
Var(X) =
4.Medium
xp(x)00.310.3520.35μ = 1.05

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
σ =
5.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = 5X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = 5X + 1
σY =
6.Hard
n = 5, p = 0.1: P(X ≤ 1) = ?k012345

5 components are tested, and each one fails with probability 0.1, independently. What is the probability P that at most one fails?

n = 5p = 0.1
P =

Answer key

  1. 1. E(X) = 1
  2. 2. P(X = 1) = 0.3
  3. 3. Var(X) = 1.287
  4. 4. σ = 0.8047
  5. 5. σY = 4.183
  6. 6. P = 0.9185

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