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)100.1200.35300.25400.3

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

x: 10, 20, 30, 40p(x): 0.1, 0.35, 0.25, 0.3
E(X) =
2.Easy
red: 2blue: 2green: 1

A bag holds 2 red, 2 blue and 1 green balls. You draw one at random. What is the probability P that it is red?

2 / 2 / 1
P =
3.Medium
xp(x)00.2520.2540.360.2μ = 2.9

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

x: 0, 2, 4, 6p(x): 0.25, 0.25, 0.3, 0.2
σ =
4.Medium
n = 15k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 15? The order does not matter.

n = 15k = 4
N =
5.Hard
n = 12, p = 0.7: P(X = 3) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 3 correct answers?

n = 12p = 0.7k = 3
P =
6.Hard
xp(x)00.210.220.3530.0540.2μ

X has the distribution shown, and Y = 0.5X + 20. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.2, 0.2, 0.35, 0.05, 0.2Y = 0.5X + 20
σY =

Answer key

  1. 1. E(X) = 27.5
  2. 2. P = 0.4
  3. 3. σ = 2.142
  4. 4. N = 1365
  5. 5. P = 0.001485
  6. 6. σY = 0.6759

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