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: 3blue: 6green: 1

A bag holds 3 red, 6 blue and 1 green balls. You draw one at random. What is the probability P that it is red?

3 / 6 / 1
P =
2.Easy
xp(x)00.3520.140.260.35

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

x: 0, 2, 4, 6p(x): 0.35, 0.1, 0.2, 0.35
E(X) =
3.Medium
xp(x)00.220.3540.260.25μ = 3

For the distribution shown, find the variance Var(X) of X.

x: 0, 2, 4, 6p(x): 0.2, 0.35, 0.2, 0.25
Var(X) =
4.Medium
red: 4blue: 3

A bag holds 4 red and 3 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

4 / 3
P =
5.Hard
xp(x)00.3510.320.35μ

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = 3X + 1
σY =
6.Hard
n = 8, p = 0.2: P(X = 5) = ?k012345678

A test has 8 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 5 correct answers?

n = 8p = 0.2k = 5
P =

Answer key

  1. 1. P = 0.3
  2. 2. E(X) = 3.1
  3. 3. Var(X) = 4.6
  4. 4. P = 0.2857
  5. 5. σY = 2.51
  6. 6. P = 0.009175

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