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: 3green: 2

A bag holds 8 red, 3 blue and 2 green balls. You draw one at random. What is the probability P that it is red?

8 / 3 / 2
P =
2.Easy
xp(x)0?20.340.2560.1

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 2, 4, 6p(x): ?, 0.3, 0.25, 0.1
P(X = 0) =
3.Medium
n = 9k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 9? The order does not matter.

n = 9k = 2
N =
4.Medium
n = 8k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 8? The order does not matter.

n = 8k = 5
N =
5.Hard
xp(x)00.1510.3520.1530.35μ

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

x: 0, 1, 2, 3p(x): 0.15, 0.35, 0.15, 0.35Y = −2X + 20
σY =
6.Hard
n = 7, p = 0.4: P(X = 2) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.4, independently. What is the probability P of exactly 2 correct answers?

n = 7p = 0.4k = 2
P =

Answer key

  1. 1. P = 0.6154
  2. 2. P(X = 0) = 0.35
  3. 3. N = 36
  4. 4. N = 56
  5. 5. σY = 2.2
  6. 6. P = 0.2613

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