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: 7

A bag holds 6 red and 7 blue balls. You draw one at random. What is the probability P that it is not red?

6 / 7
P =
2.Easy
xp(x)10.1520.230.140.3550.2

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

x: 1, 2, 3, 4, 5p(x): 0.15, 0.2, 0.1, 0.35, 0.2
E(X) =
3.Medium
xp(x)00.1510.2520.1530.340.15μ = 2.05

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

x: 0, 1, 2, 3, 4p(x): 0.15, 0.25, 0.15, 0.3, 0.15
σ =
4.Medium
n = 6k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 6? The order does not matter.

n = 6k = 2
N =
5.Hard
xp(x)100.3200.15300.35400.2μ

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

x: 10, 20, 30, 40p(x): 0.3, 0.15, 0.35, 0.2Y = 2X + 10
σY =
6.Hard
xp(x)00.2510.1520.2530.35μ

X has the distribution shown, and Y = 2X + 5. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.25, 0.15, 0.25, 0.35Y = 2X + 5
σY =

Answer key

  1. 1. P = 0.5385
  2. 2. E(X) = 3.25
  3. 3. σ = 1.322
  4. 4. N = 15
  5. 5. σY = 22.34
  6. 6. σY = 2.375

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