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: 4blue: 4green: 4

A bag holds 4 red, 4 blue and 4 green balls. You draw one at random. What is the probability P that it is not red?

4 / 4 / 4
P =
2.Easy
xp(x)00.22?40.1560.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 0, 2, 4, 6p(x): 0.2, ?, 0.15, 0.3
P(X = 2) =
3.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 =
4.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
σ =
5.Hard
n = 5, p = 0.25: P(X = 2) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 2 correct answers?

n = 5p = 0.25k = 2
P =
6.Hard
xp(x)10.320.230.2540.25μ

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

x: 1, 2, 3, 4p(x): 0.3, 0.2, 0.25, 0.25Y = 5X + 5
σY =

Answer key

  1. 1. P = 0.6667
  2. 2. P(X = 2) = 0.35
  3. 3. P = 0.3056
  4. 4. σ = 0.8047
  5. 5. P = 0.2637
  6. 6. σY = 5.804

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