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)10.120.330.140.1550.35

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

x: 1, 2, 3, 4, 5p(x): 0.1, 0.3, 0.1, 0.15, 0.35
E(X) =
2.Easy
sum ≥ 10die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 10?

2 dice≥ 10
P =
3.Medium
xp(x)10.3520.2530.340.1μ = 2.15

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

x: 1, 2, 3, 4p(x): 0.35, 0.25, 0.3, 0.1
σ =
4.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) =
5.Hard
xp(x)10.1520.330.240.1550.2μ

X has the distribution shown, and Y = 10X + 20. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.15, 0.3, 0.2, 0.15, 0.2Y = 10X + 20
σY =
6.Hard
n = 10, p = 0.5: P(X = 2) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 2 correct answers?

n = 10p = 0.5k = 2
P =

Answer key

  1. 1. E(X) = 3.35
  2. 2. P = 0.1667
  3. 3. σ = 1.014
  4. 4. Var(X) = 0.7
  5. 5. σY = 13.59
  6. 6. P = 0.04395

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