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)00.320.3540.1560.2

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

x: 0, 2, 4, 6p(x): 0.3, 0.35, 0.15, 0.2
E(X) =
2.Easy
xp(x)00.210.1520.053?40.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 0, 1, 2, 3, 4p(x): 0.2, 0.15, 0.05, ?, 0.3
P(X = 3) =
3.Medium
xp(x)00.2520.340.160.35μ = 3.1

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

x: 0, 2, 4, 6p(x): 0.25, 0.3, 0.1, 0.35
σ =
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)00.3510.1520.2530.25μ

X has the distribution shown, and Y = 0.5X + 4. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.35, 0.15, 0.25, 0.25Y = 0.5X + 4
σY =
6.Hard
n = 5, p = 0.25: P(X = 4) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 4 correct answers?

n = 5p = 0.25k = 4
P =

Answer key

  1. 1. E(X) = 2.5
  2. 2. P(X = 3) = 0.3
  3. 3. σ = 2.406
  4. 4. P = 0.3182
  5. 5. σY = 0.6
  6. 6. P = 0.01465

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