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
sum ≥ 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 11?

2 dice≥ 11
P =
2.Easy
xp(x)100.25200.25300.15400.35

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

x: 10, 20, 30, 40p(x): 0.25, 0.25, 0.15, 0.35
E(X) =
3.Medium
xp(x)10.320.3530.140.25μ = 2.3

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

x: 1, 2, 3, 4p(x): 0.3, 0.35, 0.1, 0.25
Var(X) =
4.Medium
red: 3blue: 4

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

3 / 4
P =
5.Hard
xp(x)10.320.2530.340.15μ

X has the distribution shown, and Y = −2X + 20. Find the standard deviation σY of Y.

x: 1, 2, 3, 4p(x): 0.3, 0.25, 0.3, 0.15Y = −2X + 20
σY =
6.Hard
n = 10, p = 0.3: P(X = 2) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 2 correct answers?

n = 10p = 0.3k = 2
P =

Answer key

  1. 1. P = 0.08333
  2. 2. E(X) = 26
  3. 3. Var(X) = 1.31
  4. 4. P = 0.1429
  5. 5. σY = 2.107
  6. 6. P = 0.2335

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