# Find the probability of observing an event.

PROBLEM 1

PART ONE

In a shipment of 15 room air conditioners, there are 3 with defective thermostats. Two air conditioners will be selected at random and inspected one after another. Find the probability that

(a) The first is defective.

(b) The first is defective and the second is good.

(c) Both are defective.

(d) The second air conditioner is defective.

(e) Exactly one is defective.

PART TWO

Now suppose 3 air conditioners will be selected at random and checked one after another. Find the probability that

(a) All three are good.

(b) The first 2 are good and the third is defective.

(c) Two are good and 1 is defective.

https://brainmass.com/statistics/probability/find-the-probability-of-observing-an-event-12801

#### Solution Preview

PROBLEM 1

PART ONE

In a shipment of 15 room air conditioners, there are 3 with defective thermostats. Two air conditioners will be selected at random and inspected one after another. Find the probability that

(a) The first is defective.

Since there are 3 defective and 15 air conditioners in total,

P (the first is defective) = 3/15 = 1/5 = 0.20

(b) The first is defective and the second is good.

Given that the first is defective, P = 3/15, and the second is good, P = 12 / 14

P (first is defective and the second is good) = ...

#### Solution Summary

The following question outlines the process for determining the probability of observing an event. This probabilities are solved in the context of a quality assurance problem.