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)10.220.2530.2540.250.1

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

x: 1, 2, 3, 4, 5p(x): 0.2, 0.25, 0.25, 0.2, 0.1
E(X) =
2.Easy
sum = 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 4?

2 dice= 4
P =
3.Medium
xp(x)00.1510.220.3530.3μ = 1.8

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

x: 0, 1, 2, 3p(x): 0.15, 0.2, 0.35, 0.3
Var(X) =
4.Medium
red: 8blue: 8

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

8 / 8
P =
5.Hard
xp(x)00.210.1520.2530.0540.35μ

X has the distribution shown, and Y = 3X + 5. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.2, 0.15, 0.25, 0.05, 0.35Y = 3X + 5
σY =
6.Hard
€p(x)−20.7880.2380.02

A game costs €2 to play. You win €10 with probability 0.2 and €40 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€10: p = 0.2€40: p = 0.02
E(G) = €

Answer key

  1. 1. E(X) = 2.75
  2. 2. P = 0.08333
  3. 3. Var(X) = 1.06
  4. 4. P = 0.2333
  5. 5. σY = 4.609
  6. 6. E(G) = 0.8 €

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