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: 5green: 5

A bag holds 5 red, 5 blue and 5 green balls. You draw one at random. What is the probability P that it is not red?

5 / 5 / 5
P =
2.Easy
xp(x)10.32?30.2540.150.2

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

x: 1, 2, 3, 4, 5p(x): 0.3, ?, 0.25, 0.1, 0.2
P(X = 2) =
3.Medium
xp(x)00.2510.320.0530.340.1μ = 1.7

For the distribution shown, find the variance Var(X) of X.

x: 0, 1, 2, 3, 4p(x): 0.25, 0.3, 0.05, 0.3, 0.1
Var(X) =
4.Medium
red: 7blue: 3

A bag holds 7 red and 3 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 3
P =
5.Hard
n = 6, p = 0.3: P(X ≤ 1) = ?k0123456

6 components are tested, and each one fails with probability 0.3, independently. What is the probability P that at most one fails?

n = 6p = 0.3
P =
6.Hard
xp(x)00.2520.140.360.35μ

X has the distribution shown, and Y = 0.5X + 4. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.25, 0.1, 0.3, 0.35Y = 0.5X + 4
σY =

Answer key

  1. 1. P = 0.6667
  2. 2. P(X = 2) = 0.15
  3. 3. Var(X) = 1.91
  4. 4. P = 0.4667
  5. 5. P = 0.4202
  6. 6. σY = 1.178

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