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)00.3510.352?

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

x: 0, 1, 2p(x): 0.35, 0.35, ?
P(X = 2) =
2.Easy
sum = 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 4?

2 dice= 4
P =
3.Medium
xp(x)00.3520.0540.360.3μ = 3.1

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

x: 0, 2, 4, 6p(x): 0.35, 0.05, 0.3, 0.3
σ =
4.Medium
red: 3blue: 7

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

3 / 7
P =
5.Hard
xp(x)100.3200.35300.25400.1μ

X has the distribution shown, and Y = 0.5X + 20. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.3, 0.35, 0.25, 0.1Y = 0.5X + 20
σY =
6.Hard
n = 12, p = 0.7: P(X ≤ 1) = ?k0123456789101112

12 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 12p = 0.7
P =

Answer key

  1. 1. P(X = 2) = 0.3
  2. 2. P = 0.08333
  3. 3. σ = 2.488
  4. 4. P = 0.06667
  5. 5. σY = 4.815
  6. 6. P = 1.541 × 10⁻⁵

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