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: 2

A bag holds 6 red and 2 blue balls. You draw one at random. What is the probability P that it is not red?

6 / 2
P =
2.Easy
xp(x)00.1520.2540.36?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 6).

x: 0, 2, 4, 6p(x): 0.15, 0.25, 0.3, ?
P(X = 6) =
3.Medium
n = 7k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 7? The order does not matter.

n = 7k = 4
N =
4.Medium
xp(x)10.220.3530.140.250.15μ = 2.75

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

x: 1, 2, 3, 4, 5p(x): 0.2, 0.35, 0.1, 0.2, 0.15
Var(X) =
5.Hard
n = 10, p = 0.7: P(X ≤ 1) = ?k012345678910

10 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 10p = 0.7
P =
6.Hard
xp(x)00.0510.120.2530.340.3μ

X has the distribution shown, and Y = 3X + 5. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.05, 0.1, 0.25, 0.3, 0.3Y = 3X + 5
σY =

Answer key

  1. 1. P = 0.25
  2. 2. P(X = 6) = 0.3
  3. 3. N = 35
  4. 4. Var(X) = 1.887
  5. 5. P = 0.0001437
  6. 6. σY = 3.434

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