Presentation For Probability

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Burger preferences (Problem 2.19)

A 2010 SurveyUSA poll asked 500 Los Angeles residents, “What is the best hamburger place in Southern California? Five Guys Burgers? In-N-Out Burger? Fat Burger? Tommy’s Hamburgers? Umami Burger? Or somewhere else?” The distribution of responses by gender is shown below.

1. Are being female and liking Five Guys Burgers mutually exclusive?
2. What is the probability that a randomly chosen male likes In-N-Out the best?
3. What is the probability that a randomly chosen female likes In-N-Out the best?
4. What is the probability that a man and a woman who are dating both like In-N-Out the best? Note any assumption you make and evaluate whether you think that assumption is reasonable.
5. What is the probability that a randomly chosen person likes Umami best or that person is female?

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Best Hamburger Place !

Burger Joint	Male	Female	Total
	5	6	11
	162	181	343
	10	12	22
	27	27	54
	5	1	6
Other	26	20	46
Not Sure	13	5	18
Total	248	252	500

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(a) Are being female and liking Five Guys Burgers mutually exclusive?

Solution:

Out of the total surveyed, 11 members like Five Guys Burgers and we have 6 of them as females. This means that the group of those who like Five Guys Burgers and female group overlaps. Since they are not disjoint, they are not mutually exclusive.

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(b) What is the probability that a randomly chosen male likes In-N-Out the best?

Solution:

There are total 248 male members surveyed. Out of these 162 like the burgers from In-N-Out the best. So if we randomly choose a male, the probaility that he may be liking In-N-Out burgers is

P(male liking In-N-Out)
= 162 / 248
= 0.6532 ~ 0.65

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(c) What is the probability that a randomly chosen female likes In-N-Out the best?

Solution:

There are total 252 female members in the survey. Out of these 181 like the burgers from In-N-Out the best. So if we randomly choose a female, the probaility that she may be liking In-N-Out burgers is

P(female liking In-N-Out)
= 181 / 252
= 0.7182 ~ 0.72

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(d) What is the probability that a man and a woman who are dating both like In-N-Out the best?

Note any assumption you make and evaluate whether you think that assumption is reasonable.

Solution:

The burger fondness for In-N-Out for either a male of female member would be independent. And hence probability of both liking In-N-Out burgers can be calculated as

P(Both male and female liking In-N-Out)
= P(male liking In-N-Out) * P(female liking In-N-Out)
= 0.65 * 0.72
= 0.468

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(e) What is the probability that a randomly chosen person likes Umami best or that person is female?

Solution:

Out of the total 500 members surveyed, those who liked Umami Burgers are only 6. From this set of 6, we know there are 5 male and 1 female member.

Since those who like Umami and those who are females have 1 member in common i.e. 1 female member liking Umami burger, we need to remove the repetetive value

P(a person chosen likes Umami burger OR person is a female)
= P(a person chosen likes Umami burger ) + P(person chosen is female )
- P(person chosen is a female liking Umami burger)
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Total members surveyed
= (6 + 252 - 1 ) / 500
= 257/ 500
= 0.514

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