.19 Burger preferences. A 2010 Survey USA poll asked 500 Los Angeles residents,

Question

.19 Burger preferences. A 2010 Survey USA 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.6 Gender emale Total ve Guys Burgers In-N-Out Burger Fat Burger 162 10 27 6 181 12 27 343 Best hamburger Tommy's Hamburge 54 6 46 18 500 rs Umami Burger Other Not Sure Total 26 13 248 20 252 (a) Are being female and liking Five Guys Burgers mutually exclusive? (b) What is the probability that a randomly chosen male likes In-N-Out the best? (c) What is the probability that a randomly chosen female likes In-N-Out the best? 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. (e) What is the probability that a randomly chosen person likes Umami best or that person is female?

Explanation / Answer

a)

No as they contains 6 common elements therefore these can not be mutually exclusive

b)

P(In n out|male) =162/248=81/124=0.6532

c)

P(In n out|female) =181/252=0.7183

d)

we assume that events are independent

therefore P(both like In n out the best)=(81/124)*(181/252)=0.4692

e)

P(like Umami or female)=P(Umami)+P(female)-P(Umami and female)=(6+252-1)/500=247/500

=0.494

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