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)00.051?20.3530.25

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

x: 0, 1, 2, 3p(x): 0.05, ?, 0.35, 0.25
P(X = 1) =
2.Easy
red: 2blue: 2

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

2 / 2
P =
3.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 =
4.Medium
n = 9k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 9? The order does not matter.

n = 9k = 5
N =
5.Hard
xp(x)00.0520.3540.2560.35μ

X has the distribution shown, and Y = 5X + 4. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.05, 0.35, 0.25, 0.35Y = 5X + 4
σY =
6.Hard
n = 6, p = 0.25: P(X ≤ 1) = ?k0123456

6 components are tested, and each one fails with probability 0.25, independently. What is the probability P that at most one fails?

n = 6p = 0.25
P =

Answer key

  1. 1. P(X = 1) = 0.35
  2. 2. P = 0.5
  3. 3. P = 0.5177
  4. 4. N = 126
  5. 5. σY = 9.434
  6. 6. P = 0.5339

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