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)100.25200.330?400.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 30).

x: 10, 20, 30, 40p(x): 0.25, 0.3, ?, 0.35
P(X = 30) =
2.Easy
red: 7blue: 2green: 1

A bag holds 7 red, 2 blue and 1 green balls. You draw one at random. What is the probability P that it is red?

7 / 2 / 1
P =
3.Medium
red: 7blue: 7

A bag holds 7 red and 7 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 7
P =
4.Medium
P(at least one six) = ??1?2?3P(six) = 1/6 on each roll

A fair die is rolled 3 times. What is the probability P of getting at least one six?

n = 3
P =
5.Hard
xp(x)100.35200.15300.25400.25μ

X has the distribution shown, and Y = 10X − 3. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.35, 0.15, 0.25, 0.25Y = 10X − 3
σY =
6.Hard
n = 10, p = 0.5: P(X = 5) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 5 correct answers?

n = 10p = 0.5k = 5
P =

Answer key

  1. 1. P(X = 30) = 0.1
  2. 2. P = 0.7
  3. 3. P = 0.2308
  4. 4. P = 0.4213
  5. 5. σY = 120
  6. 6. P = 0.2461

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