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)00.120.34?60.25

The table gives the probability distribution of X, but one probability is missing. Find P(X = 4).

x: 0, 2, 4, 6p(x): 0.1, 0.3, ?, 0.25
P(X = 4) =
2.Easy
xp(x)100.35200.15300.15400.35

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

x: 10, 20, 30, 40p(x): 0.35, 0.15, 0.15, 0.35
E(X) =
3.Medium
xp(x)00.1520.340.360.25μ = 3.3

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

x: 0, 2, 4, 6p(x): 0.15, 0.3, 0.3, 0.25
σ =
4.Medium
red: 7blue: 4

A bag holds 7 red and 4 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 4
P =
5.Hard
n = 9, p = 0.6: P(X ≤ 1) = ?k0123456789

9 components are tested, and each one fails with probability 0.6, independently. What is the probability P that at most one fails?

n = 9p = 0.6
P =
6.Hard
xp(x)100.05200.35300.3400.3μ

X has the distribution shown, and Y = 10X + 20. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.05, 0.35, 0.3, 0.3Y = 10X + 20
σY =

Answer key

  1. 1. P(X = 4) = 0.35
  2. 2. E(X) = 25
  3. 3. σ = 2.027
  4. 4. P = 0.3818
  5. 5. P = 0.003801
  6. 6. σY = 90.97

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