According to the U.S. Census Bureau, the probability a...

According to the U.S. Census Bureau, the probability a randomly selected worker primarily drives a car to work is $0.82 .$ The probability a randomly selected worker primarily takes public transportation to work is 0.053 (a) What is the probability a randomly selected worker primarily drives a car or takes public transportation to work? (b) What is the probability a randomly selected worker neither drives a car nor takes public transportation to work? (c) What is the probability a randomly selected worker does not drive a car to work? (d) Can the probability a randomly selected worker walks to work equal 0.15? Why or why not?

According to the U.S. Census Bureau, the probability a randomly selected worker primarily drives a car to work is $0.82 .$ The probability a randomly selected worker primarily takes public transportation to work is 0.053
(a) What is the probability a randomly selected worker primarily drives a car or takes public transportation
to work?
(b) What is the probability a randomly selected worker neither drives a car nor takes public transportation to work?
(c) What is the probability a randomly selected worker does not drive a car to work?
(d) Can the probability a randomly selected worker walks to work equal 0.15? Why or why not?

Key Concepts

Probability Constraints

Probability constraints dictate that the sum of probabilities for all mutually exclusive and exhaustive outcomes must equal one, and no individual probability can be negative or exceed one. This ensures consistency within any probability model and helps identify when a proposed probability assignment is infeasible.

Complement Rule

The complement rule is a fundamental concept in probability stating that the probability of an event not occurring is equal to one minus the probability that the event does occur. It is often used to simplify probability calculations by focusing on what does not happen.

Addition Rule for Probabilities

This rule states that the probability of the union of two events (i.e., the chance that at least one of the events occurs) is equal to the sum of the probabilities of the individual events when the events are mutually exclusive, meaning they cannot both happen at the same time.

Transcript

00:03 Hello hi here in this question we have been given a probability data in that probability that a selected worker will be driving a car to work so you'll be using car to work i'm calling that event as c i can say b of c that is using car is given 0 .82 now the second event is given a randomly selected worker will be using public transportation.

00:43 Public transportation.

00:45 That probability i am calling us, probability of p, p for public transportation is given 0 .053.

00:56 Okay, these two data are given.

00:59 Now the question is asking what is the probability that a randomly selected worker will be drives a car or take a public transportation.

01:08 That means we have to find c or p.

01:13 You know, it is given by p of c plus p of p of p minus p of c intersection p.

01:19 But if a person is going by car, he won't be using public transportation.

01:24 So this value particularly becomes zero, since you cannot use both.

01:31 So we just have to add these two.

01:33 When you add these two, we see what value we get.

01:38 So we have to add 0 .82 plus 0 .8 .2.

01:44 0 .053, 0 .873.

01:49 This will be the required answer for the first part of the question.

01:53 Now in the second part, it's asking what is the probability that the selected worker, neither use a car nor public transportation.

02:04 That means we have to find c or p, we already found out.

02:10 We have to find a complement of that event.

02:14 So complement of an event is given by 1 minus probability of that event...

Please give Ace some feedback