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: 3green: 5

A bag holds 4 red, 3 blue and 5 green balls. You draw one at random. What is the probability P that it is blue?

4 / 3 / 5
P =
2.Easy
xp(x)100.15200.3300.3540?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 40).

x: 10, 20, 30, 40p(x): 0.15, 0.3, 0.35, ?
P(X = 40) =
3.Medium
n = 11k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 11? The order does not matter.

n = 11k = 5
N =
4.Medium
xp(x)00.1510.320.2530.1540.15μ = 1.85

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

x: 0, 1, 2, 3, 4p(x): 0.15, 0.3, 0.25, 0.15, 0.15
σ =
5.Hard
n = 6, p = 0.2: P(X ≤ 1) = ?k0123456

6 components are tested, and each one fails with probability 0.2, independently. What is the probability P that at most one fails?

n = 6p = 0.2
P =
6.Hard
xp(x)100.35200.35300.15400.15μ

X has the distribution shown, and Y = 0.5X + 1. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.35, 0.35, 0.15, 0.15Y = 0.5X + 1
σY =

Answer key

  1. 1. P = 0.25
  2. 2. P(X = 40) = 0.2
  3. 3. N = 462
  4. 4. σ = 1.276
  5. 5. P = 0.6554
  6. 6. σY = 5.22

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