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
red: 2blue: 5green: 5

A bag holds 2 red, 5 blue and 5 green balls. You draw one at random. What is the probability P that it is blue?

2 / 5 / 5
P =
2.Easy
xp(x)1?20.230.340.3

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

x: 1, 2, 3, 4p(x): ?, 0.2, 0.3, 0.3
P(X = 1) =
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)00.210.3520.230.25μ = 1.5

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

x: 0, 1, 2, 3p(x): 0.2, 0.35, 0.2, 0.25
σ =
5.Hard
n = 6, p = 0.5: P(X = 4) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 4 correct answers?

n = 6p = 0.5k = 4
P =
6.Hard
xp(x)00.320.2540.160.35μ

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

x: 0, 2, 4, 6p(x): 0.3, 0.25, 0.1, 0.35Y = 10X + 4
σY =

Answer key

  1. 1. P = 0.4167
  2. 2. P(X = 1) = 0.2
  3. 3. P = 0.5981
  4. 4. σ = 1.072
  5. 5. P = 0.2344
  6. 6. σY = 24.9

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