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
red: 6blue: 5green: 5

A bag holds 6 red, 5 blue and 5 green balls. You draw one at random. What is the probability P that it is blue?

6 / 5 / 5
P =
2.Easy
xp(x)10.220.1530.240.250.25

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

x: 1, 2, 3, 4, 5p(x): 0.2, 0.15, 0.2, 0.2, 0.25
E(X) =
3.Medium
P(at least one six) = ??1?2?3?4?5P(six) = 1/6 on each roll

A fair die is rolled 5 times. What is the probability P of getting at least one six?

n = 5
P =
4.Medium
n = 10k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 10? The order does not matter.

n = 10k = 2
N =
5.Hard
€p(x)−20.6880.3180.02

A game costs €2 to play. You win €10 with probability 0.3 and €20 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€10: p = 0.3€20: p = 0.02
E(G) = €
6.Hard
xp(x)00.3520.2540.3560.05μ

X has the distribution shown, and Y = 2X + 10. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.35, 0.25, 0.35, 0.05Y = 2X + 10
σY =

Answer key

  1. 1. P = 0.3125
  2. 2. E(X) = 3.15
  3. 3. P = 0.5981
  4. 4. N = 45
  5. 5. E(G) = 1.4 €
  6. 6. σY = 3.774

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