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: 4blue: 6green: 2

A bag holds 4 red, 6 blue and 2 green balls. You draw one at random. What is the probability P that it is red?

4 / 6 / 2
P =
2.Easy
xp(x)00.3510.3520.230.1

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

x: 0, 1, 2, 3p(x): 0.35, 0.35, 0.2, 0.1
E(X) =
3.Medium
xp(x)00.310.320.0530.35μ = 1.45

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

x: 0, 1, 2, 3p(x): 0.3, 0.3, 0.05, 0.35
σ =
4.Medium
red: 4blue: 8

A bag holds 4 red and 8 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

4 / 8
P =
5.Hard
n = 9, p = 0.4: P(X = 3) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.4, independently. What is the probability P of exactly 3 correct answers?

n = 9p = 0.4k = 3
P =
6.Hard
xp(x)00.310.3520.35μ

X has the distribution shown, and Y = 10X + 20. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.3, 0.35, 0.35Y = 10X + 20
σY =

Answer key

  1. 1. P = 0.3333
  2. 2. E(X) = 1.05
  3. 3. σ = 1.244
  4. 4. P = 0.09091
  5. 5. P = 0.2508
  6. 6. σY = 8.047

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