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)00.351?20.35

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

x: 0, 1, 2p(x): 0.35, ?, 0.35
P(X = 1) =
2.Easy
red: 8blue: 8green: 5

A bag holds 8 red, 8 blue and 5 green balls. You draw one at random. What is the probability P that it is blue?

8 / 8 / 5
P =
3.Medium
xp(x)10.220.1530.340.0550.3μ = 3.1

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

x: 1, 2, 3, 4, 5p(x): 0.2, 0.15, 0.3, 0.05, 0.3
Var(X) =
4.Medium
P(at least one six) = ??1?2P(six) = 1/6 on each roll

A fair die is rolled 2 times. What is the probability P of getting at least one six?

n = 2
P =
5.Hard
n = 9, p = 0.1: P(X = 4) = ?k0123456789

A test has 9 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 = 9p = 0.1k = 4
P =
6.Hard
xp(x)00.3510.3520.3μ

X has the distribution shown, and Y = 0.5X + 5. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.35, 0.3Y = 0.5X + 5
σY =

Answer key

  1. 1. P(X = 1) = 0.3
  2. 2. P = 0.381
  3. 3. Var(X) = 2.19
  4. 4. P = 0.3056
  5. 5. P = 0.00744
  6. 6. σY = 0.4023

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