You order twelve burritos to go from a Mexican restaurant, five with hot peppers and seven without. However, the restaurant forgot to label them. You pick three burritos at random. Find the probability of the events (as a reduced fraction and as a percent rounded to the nearest tenth of a percent).

Question

a) All 3 of the burritos have hot peppers.
b) None of the three burritos have hot peppers.
c) Exactly one of the three burritos has hot peppers.
d) Exactly two of the three burritos have hot peppers.
e) At least one of the three burritos has hot peppers.
f) At least two of the three burritos have hot peppers.
g) At most two of the three burritos have hot peppers.

Answer 1

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

P(3) = (5/12)^3

P(1of3) = (5/12)(7/12)^2

e) At least one = one, two or three

Either-or probabilities are found by adding the individual probabilities.