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: 2green: 2

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

4 / 2 / 2
P =
2.Easy
xp(x)00.1510.0520.3530.140.35

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

x: 0, 1, 2, 3, 4p(x): 0.15, 0.05, 0.35, 0.1, 0.35
E(X) =
3.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
Var(X) =
4.Medium
red: 7blue: 5

A bag holds 7 red and 5 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 5
P =
5.Hard
xp(x)00.2510.320.330.15μ

X has the distribution shown, and Y = 10X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.25, 0.3, 0.3, 0.15Y = 10X + 1
σY =
6.Hard
n = 6, p = 0.2: P(X = 4) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 4 correct answers?

n = 6p = 0.2k = 4
P =

Answer key

  1. 1. P = 0.5
  2. 2. E(X) = 2.45
  3. 3. Var(X) = 0.6475
  4. 4. P = 0.3182
  5. 5. σY = 10.14
  6. 6. P = 0.01536

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