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)10.320.230.140.0550.35

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.2, 0.1, 0.05, 0.35
E(X) =
2.Easy
xp(x)00.252?40.3560.35

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

x: 0, 2, 4, 6p(x): 0.25, ?, 0.35, 0.35
P(X = 2) =
3.Medium
xp(x)00.310.1520.1530.340.1μ = 1.75

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

x: 0, 1, 2, 3, 4p(x): 0.3, 0.15, 0.15, 0.3, 0.1
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4P(six) = 1/6 on each roll

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
5.Hard
xp(x)100.15200.25300.35400.25μ

X has the distribution shown, and Y = 10X + 4. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.15, 0.25, 0.35, 0.25Y = 10X + 4
σY =
6.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 =

Answer key

  1. 1. E(X) = 2.95
  2. 2. P(X = 2) = 0.05
  3. 3. Var(X) = 1.987
  4. 4. P = 0.5177
  5. 5. σY = 100.5
  6. 6. P = 0.4202

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