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)00.3510.320.35

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

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

A bag holds 3 red, 3 blue and 2 green balls. You draw one at random. What is the probability P that it is red?

3 / 3 / 2
P =
3.Medium
xp(x)10.0520.3530.340.3μ = 2.85

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

x: 1, 2, 3, 4p(x): 0.05, 0.35, 0.3, 0.3
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4?5?6?7P(six) = 1/6 on each roll

A fair die is rolled 7 times. What is the probability P of getting at least one six?

n = 7
P =
5.Hard
€p(x)−10.7540.2490.05

A game costs €1 to play. You win €5 with probability 0.2 and €50 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€5: p = 0.2€50: p = 0.05
E(G) = €
6.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = 2X + 20. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = 2X + 20
σY =

Answer key

  1. 1. E(X) = 1
  2. 2. P = 0.375
  3. 3. Var(X) = 0.8275
  4. 4. P = 0.7209
  5. 5. E(G) = 2.5 €
  6. 6. σY = 1.673

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