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)100.15200.25300.3400.3

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

x: 10, 20, 30, 40p(x): 0.15, 0.25, 0.3, 0.3
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 red?

3 / 4 / 2
P =
3.Medium
xp(x)00.1510.320.2530.2540.05μ = 1.75

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

x: 0, 1, 2, 3, 4p(x): 0.15, 0.3, 0.25, 0.25, 0.05
Var(X) =
4.Medium
n = 9k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 9? The order does not matter.

n = 9k = 3
N =
5.Hard
€p(x)−100.69400.34900.01

A game costs €10 to play. You win €50 with probability 0.3 and €500 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€50: p = 0.3€500: p = 0.01
E(G) = €
6.Hard
xp(x)100.35200.2300.2400.25μ

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

x: 10, 20, 30, 40p(x): 0.35, 0.2, 0.2, 0.25Y = 3X + 10
σY =

Answer key

  1. 1. E(X) = 27.5
  2. 2. P = 0.3333
  3. 3. Var(X) = 1.287
  4. 4. N = 84
  5. 5. E(G) = 10 €
  6. 6. σY = 35.84

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