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)00.220.340.360.2

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

x: 0, 2, 4, 6p(x): 0.2, 0.3, 0.3, 0.2
E(X) =
2.Easy
red: 4blue: 4green: 2

A bag holds 4 red, 4 blue and 2 green balls. You draw one at random. What is the probability P that it is red?

4 / 4 / 2
P =
3.Medium
xp(x)10.320.0530.340.350.05μ = 2.75

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.05, 0.3, 0.3, 0.05
σ =
4.Medium
xp(x)10.320.330.140.3μ = 2.4

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

x: 1, 2, 3, 4p(x): 0.3, 0.3, 0.1, 0.3
Var(X) =
5.Hard
€p(x)−30.7830.21470.02

A game costs €3 to play. You win €6 with probability 0.2 and €150 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€6: p = 0.2€150: p = 0.02
E(G) = €
6.Hard
xp(x)100.15200.35300.35400.15μ

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

x: 10, 20, 30, 40p(x): 0.15, 0.35, 0.35, 0.15Y = 5X − 3
σY =

Answer key

  1. 1. E(X) = 3
  2. 2. P = 0.4
  3. 3. σ = 1.299
  4. 4. Var(X) = 1.44
  5. 5. E(G) = 1.2 €
  6. 6. σY = 46.1

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