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: 5blue: 6green: 5

A bag holds 5 red, 6 blue and 5 green balls. You draw one at random. What is the probability P that it is red?

5 / 6 / 5
P =
2.Easy
xp(x)10.320.3530.340.05

A random variable X has the probability distribution shown. Find its expected value E(X).

x: 1, 2, 3, 4p(x): 0.3, 0.35, 0.3, 0.05
E(X) =
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
n = 9k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 9? The order does not matter.

n = 9k = 4
N =
5.Hard
n = 7, p = 0.4: P(X ≤ 1) = ?k01234567

7 components are tested, and each one fails with probability 0.4, independently. What is the probability P that at most one fails?

n = 7p = 0.4
P =
6.Hard
xp(x)100.15200.35300.25400.25μ

X has the distribution shown, and Y = 10X − 3. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.15, 0.35, 0.25, 0.25Y = 10X − 3
σY =

Answer key

  1. 1. P = 0.3125
  2. 2. E(X) = 2.1
  3. 3. P = 0.5981
  4. 4. N = 126
  5. 5. P = 0.1586
  6. 6. σY = 102

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