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)00.3510.3520.3

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
E(X) =
2.Easy
sum ≥ 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 11?

2 dice≥ 11
P =
3.Medium
xp(x)10.2520.3530.1540.1550.1μ = 2.5

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

x: 1, 2, 3, 4, 5p(x): 0.25, 0.35, 0.15, 0.15, 0.1
σ =
4.Medium
red: 7blue: 9

A bag holds 7 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 9
P =
5.Hard
n = 11, p = 0.7: P(X = 2) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 2 correct answers?

n = 11p = 0.7k = 2
P =
6.Hard
xp(x)00.1520.340.360.25μ

X has the distribution shown, and Y = 2X + 10. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.15, 0.3, 0.3, 0.25Y = 2X + 10
σY =

Answer key

  1. 1. E(X) = 0.95
  2. 2. P = 0.08333
  3. 3. σ = 1.285
  4. 4. P = 0.175
  5. 5. P = 0.0005305
  6. 6. σY = 4.055

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