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)00.11?20.3530.240.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 0, 1, 2, 3, 4p(x): 0.1, ?, 0.35, 0.2, 0.3
P(X = 1) =
2.Easy
red: 4blue: 5green: 3

A bag holds 4 red, 5 blue and 3 green balls. You draw one at random. What is the probability P that it is not red?

4 / 5 / 3
P =
3.Medium
red: 8blue: 9

A bag holds 8 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

8 / 9
P =
4.Medium
xp(x)00.3510.120.0530.3540.15μ = 1.85

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

x: 0, 1, 2, 3, 4p(x): 0.35, 0.1, 0.05, 0.35, 0.15
Var(X) =
5.Hard
n = 11, p = 0.1: P(X = 4) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 4 correct answers?

n = 11p = 0.1k = 4
P =
6.Hard
xp(x)00.3510.320.230.15μ

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

x: 0, 1, 2, 3p(x): 0.35, 0.3, 0.2, 0.15Y = 0.5X + 20
σY =

Answer key

  1. 1. P(X = 1) = 0.05
  2. 2. P = 0.6667
  3. 3. P = 0.2059
  4. 4. Var(X) = 2.428
  5. 5. P = 0.01578
  6. 6. σY = 0.5309

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