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)10.320.2530.2540.2

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

x: 1, 2, 3, 4p(x): 0.3, 0.25, 0.25, 0.2
E(X) =
2.Easy
sum = 10die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice= 10
P =
3.Medium
red: 7blue: 3

A bag holds 7 red and 3 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 3
P =
4.Medium
red: 3blue: 5

A bag holds 3 red and 5 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 5
P =
5.Hard
n = 6, p = 0.7: P(X = 1) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 1 correct answers?

n = 6p = 0.7k = 1
P =
6.Hard
xp(x)10.2520.330.240.150.15μ

X has the distribution shown, and Y = 5X + 4. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.25, 0.3, 0.2, 0.1, 0.15Y = 5X + 4
σY =

Answer key

  1. 1. E(X) = 2.35
  2. 2. P = 0.08333
  3. 3. P = 0.4667
  4. 4. P = 0.1071
  5. 5. P = 0.01021
  6. 6. σY = 6.782

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