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: 4blue: 7green: 3

A bag holds 4 red, 7 blue and 3 green balls. You draw one at random. What is the probability P that it is red?

4 / 7 / 3
P =
2.Easy
sum = 7die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 7?

2 dice= 7
P =
3.Medium
xp(x)00.310.120.2530.1540.2μ = 1.85

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

x: 0, 1, 2, 3, 4p(x): 0.3, 0.1, 0.25, 0.15, 0.2
Var(X) =
4.Medium
xp(x)10.220.330.240.3μ = 2.6

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

x: 1, 2, 3, 4p(x): 0.2, 0.3, 0.2, 0.3
σ =
5.Hard
xp(x)00.3510.3520.2530.05μ

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

x: 0, 1, 2, 3p(x): 0.35, 0.35, 0.25, 0.05Y = 2X + 20
σY =
6.Hard
xp(x)10.2520.3530.140.3μ

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

x: 1, 2, 3, 4p(x): 0.25, 0.35, 0.1, 0.3Y = 10X + 4
σY =

Answer key

  1. 1. P = 0.2857
  2. 2. P = 0.1667
  3. 3. Var(X) = 2.228
  4. 4. σ = 1.114
  5. 5. σY = 1.789
  6. 6. σY = 11.61

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