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)0?20.2540.260.25

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 2, 4, 6p(x): ?, 0.25, 0.2, 0.25
P(X = 0) =
2.Easy
red: 4blue: 7green: 2

A bag holds 4 red, 7 blue and 2 green balls. You draw one at random. What is the probability P that it is red?

4 / 7 / 2
P =
3.Medium
P(at least one six) = ??1?2?3?4?5P(six) = 1/6 on each roll

A fair die is rolled 5 times. What is the probability P of getting at least one six?

n = 5
P =
4.Medium
xp(x)00.1520.3540.260.3μ = 3.3

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

x: 0, 2, 4, 6p(x): 0.15, 0.35, 0.2, 0.3
σ =
5.Hard
n = 5, p = 0.6: P(X = 4) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.6, independently. What is the probability P of exactly 4 correct answers?

n = 5p = 0.6k = 4
P =
6.Hard
xp(x)100.2200.3300.15400.35μ

X has the distribution shown, and Y = 3X + 20. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.2, 0.3, 0.15, 0.35Y = 3X + 20
σY =

Answer key

  1. 1. P(X = 0) = 0.3
  2. 2. P = 0.3077
  3. 3. P = 0.5981
  4. 4. σ = 2.124
  5. 5. P = 0.2592
  6. 6. σY = 34.57

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