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)10.320.353?40.150.05

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.35, ?, 0.1, 0.05
P(X = 3) =
2.Easy
red: 8blue: 3green: 2

A bag holds 8 red, 3 blue and 2 green balls. You draw one at random. What is the probability P that it is red?

8 / 3 / 2
P =
3.Medium
red: 3blue: 5

A bag holds 3 red and 5 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 5
P =
4.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
Var(X) =
5.Hard
xp(x)100.1200.3300.25400.35μ

X has the distribution shown, and Y = 2X + 4. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.1, 0.3, 0.25, 0.35Y = 2X + 4
σY =
6.Hard
n = 11, p = 0.3: P(X ≤ 1) = ?k01234567891011

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

n = 11p = 0.3
P =

Answer key

  1. 1. P(X = 3) = 0.2
  2. 2. P = 0.6154
  3. 3. P = 0.1071
  4. 4. Var(X) = 0.6475
  5. 5. σY = 20.27
  6. 6. P = 0.113

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