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
xp(x)00.310.120.3530.25

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

x: 0, 1, 2, 3p(x): 0.3, 0.1, 0.35, 0.25
E(X) =
2.Easy
red: 4blue: 3green: 1

A bag holds 4 red, 3 blue and 1 green balls. You draw one at random. What is the probability P that it is red?

4 / 3 / 1
P =
3.Medium
xp(x)00.0510.2520.330.1540.25μ = 2.3

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

x: 0, 1, 2, 3, 4p(x): 0.05, 0.25, 0.3, 0.15, 0.25
σ =
4.Medium
xp(x)10.320.130.1540.350.15μ = 2.9

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.1, 0.15, 0.3, 0.15
Var(X) =
5.Hard
€p(x)−20.7440.25180.01

A game costs €2 to play. You win €6 with probability 0.25 and €20 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€6: p = 0.25€20: p = 0.01
E(G) = €
6.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = 10X − 3. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = 10X − 3
σY =

Answer key

  1. 1. E(X) = 1.55
  2. 2. P = 0.5
  3. 3. σ = 1.229
  4. 4. Var(X) = 2.19
  5. 5. E(G) = −0.3 €
  6. 6. σY = 8.367

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