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)00.3510.320.230.15

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

x: 0, 1, 2, 3p(x): 0.35, 0.3, 0.2, 0.15
E(X) =
2.Easy
red: 3blue: 4green: 2

A bag holds 3 red, 4 blue and 2 green balls. You draw one at random. What is the probability P that it is not red?

3 / 4 / 2
P =
3.Medium
xp(x)100.3200.1300.35400.25μ = 25.5

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

x: 10, 20, 30, 40p(x): 0.3, 0.1, 0.35, 0.25
σ =
4.Medium
red: 4blue: 3

A bag holds 4 red and 3 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

4 / 3
P =
5.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = 3X + 4. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = 3X + 4
σY =
6.Hard
€p(x)−30.75120.2270.05

A game costs €3 to play. You win €15 with probability 0.2 and €30 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€15: p = 0.2€30: p = 0.05
E(G) = €

Answer key

  1. 1. E(X) = 1.15
  2. 2. P = 0.6667
  3. 3. σ = 11.61
  4. 4. P = 0.2857
  5. 5. σY = 2.51
  6. 6. E(G) = 1.5 €

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