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
sum = 3die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 3?

2 dice= 3
P =
2.Easy
xp(x)10.3520.3530.2540.05

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

x: 1, 2, 3, 4p(x): 0.35, 0.35, 0.25, 0.05
E(X) =
3.Medium
xp(x)100.25200.3300.15400.3μ = 25

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

x: 10, 20, 30, 40p(x): 0.25, 0.3, 0.15, 0.3
Var(X) =
4.Medium
P(at least one six) = ??1?2P(six) = 1/6 on each roll

A fair die is rolled 2 times. What is the probability P of getting at least one six?

n = 2
P =
5.Hard
n = 9, p = 0.3: P(X ≤ 1) = ?k0123456789

9 components are tested, and each one fails with probability 0.3, independently. What is the probability P that at most one fails?

n = 9p = 0.3
P =
6.Hard
xp(x)00.110.2520.230.140.35μ

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

x: 0, 1, 2, 3, 4p(x): 0.1, 0.25, 0.2, 0.1, 0.35Y = 3X − 3
σY =

Answer key

  1. 1. P = 0.05556
  2. 2. E(X) = 2
  3. 3. Var(X) = 135
  4. 4. P = 0.3056
  5. 5. P = 0.196
  6. 6. σY = 4.272

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