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)00.2520.34?60.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 4).

x: 0, 2, 4, 6p(x): 0.25, 0.3, ?, 0.3
P(X = 4) =
2.Easy
xp(x)00.2510.0520.3530.35

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

x: 0, 1, 2, 3p(x): 0.25, 0.05, 0.35, 0.35
E(X) =
3.Medium
xp(x)00.2520.240.3560.2μ = 3

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

x: 0, 2, 4, 6p(x): 0.25, 0.2, 0.35, 0.2
σ =
4.Medium
xp(x)00.0510.320.3530.3μ = 1.9

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

x: 0, 1, 2, 3p(x): 0.05, 0.3, 0.35, 0.3
Var(X) =
5.Hard
xp(x)100.35200.3300.25400.1μ

X has the distribution shown, and Y = 10X + 4. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.35, 0.3, 0.25, 0.1Y = 10X + 4
σY =
6.Hard
n = 10, p = 0.1: P(X = 3) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 3 correct answers?

n = 10p = 0.1k = 3
P =

Answer key

  1. 1. P(X = 4) = 0.15
  2. 2. E(X) = 1.8
  3. 3. σ = 2.145
  4. 4. Var(X) = 0.79
  5. 5. σY = 99.5
  6. 6. P = 0.0574

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