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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Name: ____________________   Date: ____________

1.Easy
red: 7blue: 7

A bag holds 7 red and 7 blue balls. You draw one at random. What is the probability P that it is not red?

7 / 7
P =
2.Easy
xp(x)10.3520.0530.340.150.2

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

x: 1, 2, 3, 4, 5p(x): 0.35, 0.05, 0.3, 0.1, 0.2
E(X) =
3.Medium
xp(x)00.2520.3540.2560.15μ = 2.6

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

x: 0, 2, 4, 6p(x): 0.25, 0.35, 0.25, 0.15
σ =
4.Medium
xp(x)00.2510.320.1530.3μ = 1.5

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

x: 0, 1, 2, 3p(x): 0.25, 0.3, 0.15, 0.3
Var(X) =
5.Hard
€p(x)−20.7540.2980.05

A game costs €2 to play. You win €6 with probability 0.2 and €100 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€6: p = 0.2€100: p = 0.05
E(G) = €
6.Hard
xp(x)10.320.330.1540.0550.2μ

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.3, 0.15, 0.05, 0.2Y = 5X + 5
σY =

Answer key

  1. 1. P = 0.5
  2. 2. E(X) = 2.75
  3. 3. σ = 2.01
  4. 4. Var(X) = 1.35
  5. 5. E(G) = 4.2 €
  6. 6. σY = 7.327

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