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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1.Easy
xp(x)00.210.22?30.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 0, 1, 2, 3p(x): 0.2, 0.2, ?, 0.35
P(X = 2) =
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
n = 6k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 6? The order does not matter.

n = 6k = 3
N =
4.Medium
red: 6blue: 5

A bag holds 6 red and 5 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

6 / 5
P =
5.Hard
xp(x)00.210.3520.3530.1μ

X has the distribution shown, and Y = 2X − 3. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.2, 0.35, 0.35, 0.1Y = 2X − 3
σY =
6.Hard
n = 6, p = 0.6: P(X = 4) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.6, independently. What is the probability P of exactly 4 correct answers?

n = 6p = 0.6k = 4
P =

Answer key

  1. 1. P(X = 2) = 0.25
  2. 2. P = 0.1667
  3. 3. N = 20
  4. 4. P = 0.2727
  5. 5. σY = 1.819
  6. 6. P = 0.311

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