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: 8blue: 5

A bag holds 8 red and 5 blue balls. You draw one at random. What is the probability P that it is red?

8 / 5
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)10.320.330.140.1550.15μ = 2.55

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.3, 0.1, 0.15, 0.15
Var(X) =
4.Medium
n = 7k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 7? The order does not matter.

n = 7k = 2
N =
5.Hard
n = 8, p = 0.3: P(X = 3) = ?k012345678

A test has 8 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 3 correct answers?

n = 8p = 0.3k = 3
P =
6.Hard
xp(x)100.15200.35300.25400.25μ

X has the distribution shown, and Y = 3X + 10. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.15, 0.35, 0.25, 0.25Y = 3X + 10
σY =

Answer key

  1. 1. P = 0.6154
  2. 2. P = 0.1667
  3. 3. Var(X) = 2.048
  4. 4. N = 21
  5. 5. P = 0.2541
  6. 6. σY = 30.59

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