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: 5blue: 2green: 4

A bag holds 5 red, 2 blue and 4 green balls. You draw one at random. What is the probability P that it is red?

5 / 2 / 4
P =
2.Easy
xp(x)00.32?40.360.25

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 0, 2, 4, 6p(x): 0.3, ?, 0.3, 0.25
P(X = 2) =
3.Medium
xp(x)100.15200.35300.35400.15μ = 25

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

x: 10, 20, 30, 40p(x): 0.15, 0.35, 0.35, 0.15
Var(X) =
4.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 =
5.Hard
€p(x)−10.8810.1190.02

A game costs €1 to play. You win €2 with probability 0.1 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 = €1€2: p = 0.1€20: p = 0.02
E(G) = €
6.Hard
xp(x)100.35200.2300.35400.1μ

X has the distribution shown, and Y = 10X + 4. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.35, 0.2, 0.35, 0.1Y = 10X + 4
σY =

Answer key

  1. 1. P = 0.4545
  2. 2. P(X = 2) = 0.15
  3. 3. Var(X) = 85
  4. 4. P = 0.5981
  5. 5. E(G) = −0.4 €
  6. 6. σY = 103

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