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)10.220.23?40.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 1, 2, 3, 4p(x): 0.2, 0.2, ?, 0.3
P(X = 3) =
2.Easy
xp(x)00.3510.32?30.2

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

x: 0, 1, 2, 3p(x): 0.35, 0.3, ?, 0.2
P(X = 2) =
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?3?4P(six) = 1/6 on each roll

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
5.Hard
n = 6, p = 0.25: P(X = 2) = ?k0123456

A test has 6 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 = 6p = 0.25k = 2
P =
6.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = 3X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = 3X + 1
σY =

Answer key

  1. 1. P(X = 3) = 0.3
  2. 2. P(X = 2) = 0.15
  3. 3. P = 0.2308
  4. 4. P = 0.5177
  5. 5. P = 0.2966
  6. 6. σY = 2.51

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