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)00.3520.34?60.15

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

x: 0, 2, 4, 6p(x): 0.35, 0.3, ?, 0.15
P(X = 4) =
2.Easy
xp(x)100.05200.3300.3540?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 40).

x: 10, 20, 30, 40p(x): 0.05, 0.3, 0.35, ?
P(X = 40) =
3.Medium
P(at least one six) = ??1?2?3?4?5?6P(six) = 1/6 on each roll

A fair die is rolled 6 times. What is the probability P of getting at least one six?

n = 6
P =
4.Medium
xp(x)10.320.230.3540.15μ = 2.35

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

x: 1, 2, 3, 4p(x): 0.3, 0.2, 0.35, 0.15
Var(X) =
5.Hard
n = 10, p = 0.2: P(X ≤ 1) = ?k012345678910

10 components are tested, and each one fails with probability 0.2, independently. What is the probability P that at most one fails?

n = 10p = 0.2
P =
6.Hard
xp(x)10.2520.330.1540.3μ

X has the distribution shown, and Y = 3X + 5. Find the standard deviation σY of Y.

x: 1, 2, 3, 4p(x): 0.25, 0.3, 0.15, 0.3Y = 3X + 5
σY =

Answer key

  1. 1. P(X = 4) = 0.2
  2. 2. P(X = 40) = 0.3
  3. 3. P = 0.6651
  4. 4. Var(X) = 1.128
  5. 5. P = 0.3758
  6. 6. σY = 3.486

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