Q. Cooper Realty is a small real estate company located in Albany New York, spec

Question

Q. Cooper Realty is a small real estate company located in Albany New York, specializing primarily in residential listings. They recently became interested in determining the likelihood of one

of their listings being sold within a certain number of days.

  

Count of Days Price Days 1 2 3 4 Grand Total 1 81 75 65 74 295 2 59 62 64 81 266 3 62 70 49 58 239 Grand Total 202 207 178 213 800 Question 4What ishe peohability a selectod bome's initial kng price is vr $19999 Quetion SAWhat ihe peohability a selected bome's initial king price is at most S250,000 and it takes betwoen 30 ad90 days to well Quetion SBE A -Selected home's intial aking price is at most $250,000 Event Beledetakes between 30 and 90to el Are events A andB indepedet Prove using your answer to SA (i.e cell 163) Proof Question 6 If a wclocted home takes urder 30o over 90 days to well what ihe reobablity ita initial aking price is under 5150,000 o 190 999 Question7 What is the peobabeility a selected bome takes over 0D drys to er Quention Assuming a elected bone' al zak ng pnce is between S 150,000 and S199,909, what i·thc pe bab ity it takes 30 days or more to sell? Question 9A What ieblity a selected bome takes at least 30 daya do sell and i initial aking betwee S150,000 and $250,00m Quention 9BEt A -Selected home takes at least 30 drys to seL Even B-Selocted home's i price is betwcen 5150,000 and $250000. Are events A and B mutbually excluaive? Prove using your answer to 9A.e-cell 191). If mstually excluive, Question o Gove a selected home's initial aingiiso esthan 150,000, what is the probability it takes 90days ar less to sel? Question 11 What is the peobabity a selected bome takes at most 90 days to acl or its initial aking price is under $200,000

Explanation / Answer

Question 4:

Out of 800 home's, 178+213 = 391 home's asking price is over $199999 so the probability a selected home's asking price is over 199999 is

P(over $199999) = 391 / 800 = 0.48875

Question 5A:

Out of 800 home's, 59+62+64 = 185 home's asking price is atmost $250000 and sell between 30 and 90 days so the probability that home's asking price is atmost $250000 and sell between 30 and 90 days is

P(A and B) = P(atmost $250000 and sell between 30 amd 90 days) = 185 / 800 = 0.23125

Question 5B:

P(A) = P(atmost $250000) = (202 +207 +178 ) /800 = 587 /800 = 0.73375

P(B) = P(between 30 and 90 days) = 266 /800 = 0.3325

P(A)P(B) = 0.73375 * 0.3325 = 0.243971875

Since P(A and B) is not equal to P(A)P(B) so A amd B are not independent.

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