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)100.1200.25300.340?

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

x: 10, 20, 30, 40p(x): 0.1, 0.25, 0.3, ?
P(X = 40) =
2.Easy
sum = 9die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 9?

2 dice= 9
P =
3.Medium
P(at least one six) = ??1?2?3?4?5?6?7?8P(six) = 1/6 on each roll

A fair die is rolled 8 times. What is the probability P of getting at least one six?

n = 8
P =
4.Medium
xp(x)00.310.3520.35μ = 1.05

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
Var(X) =
5.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 =
6.Hard
n = 11, p = 0.7: P(X ≤ 1) = ?k01234567891011

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

n = 11p = 0.7
P =

Answer key

  1. 1. P(X = 40) = 0.35
  2. 2. P = 0.1111
  3. 3. P = 0.7674
  4. 4. Var(X) = 0.6475
  5. 5. P = 0.4202
  6. 6. P = 4.724 × 10⁻⁵

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