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
sum = 5die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 5?

2 dice= 5
P =
2.Easy
xp(x)00.320.3540.260.15

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

x: 0, 2, 4, 6p(x): 0.3, 0.35, 0.2, 0.15
E(X) =
3.Medium
xp(x)00.3510.0520.0530.240.35μ = 2.15

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

x: 0, 1, 2, 3, 4p(x): 0.35, 0.05, 0.05, 0.2, 0.35
σ =
4.Medium
n = 7k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 7? The order does not matter.

n = 7k = 5
N =
5.Hard
xp(x)00.2520.1540.360.3μ

X has the distribution shown, and Y = 3X + 1. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.25, 0.15, 0.3, 0.3Y = 3X + 1
σY =
6.Hard
n = 6, p = 0.1: P(X = 1) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 1 correct answers?

n = 6p = 0.1k = 1
P =

Answer key

  1. 1. P = 0.1111
  2. 2. E(X) = 2.4
  3. 3. σ = 1.74
  4. 4. N = 21
  5. 5. σY = 6.913
  6. 6. P = 0.3543

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