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)10.120.130.3540.350.15

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

x: 1, 2, 3, 4, 5p(x): 0.1, 0.1, 0.35, 0.3, 0.15
E(X) =
2.Easy
sum = 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice= 11
P =
3.Medium
xp(x)100.3200.05300.3400.35μ = 27

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

x: 10, 20, 30, 40p(x): 0.3, 0.05, 0.3, 0.35
Var(X) =
4.Medium
red: 8blue: 5

A bag holds 8 red and 5 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

8 / 5
P =
5.Hard
xp(x)10.1520.3530.340.2μ

X has the distribution shown, and Y = 2X + 5. Find the standard deviation σY of Y.

x: 1, 2, 3, 4p(x): 0.15, 0.35, 0.3, 0.2Y = 2X + 5
σY =
6.Hard
€p(x)−30.8860.1570.02

A game costs €3 to play. You win €9 with probability 0.1 and €60 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€9: p = 0.1€60: p = 0.02
E(G) = €

Answer key

  1. 1. E(X) = 3.3
  2. 2. P = 0.05556
  3. 3. Var(X) = 151
  4. 4. P = 0.359
  5. 5. σY = 1.947
  6. 6. E(G) = −0.9 €

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