The first three questions refer to the following information: Suppose a basketba

Question

The first three questions refer to the following information: Suppose a basketball team had a season of games with the following characteristics: 60% of all the games were at-home games. Denote this by H (the remaining were away games). 40% of all games were wins. Denote this by W (the remaining were losses). 35% of all games were at-home wins. Question 1 Of the at-home games, we are interested in finding what proportion were wins. In order to figure this out, we need to find: O P(H and W) O P(H | W) O P(W | H) O P(H) O P(W) Question 2 Again here is the information about the characteristics of a basketball team's season: 60% of all the games were at-home games. Denote this by H (the remaining were away games). 40% of all games were wins. Denote this by W (the remaining were losses). 35% of all games were at-home wins. Of the at-home games, what proportion of games were wins? (Note: Some answers are rounded to two decimal places.) O .21 O .24 O .35 O .58 O .88 Question 3 Again here is the information about the characteristics of a basketball team's season: 60% of all the games were at-home games. Denote this by H (the remaining were away games). 40% of all games were wins. Denote this by W (the remaining were losses). 35% of all games were at-home wins. If the team won a game, how likely is it that this was a home game? (Note: Some answers are rounded to 2 decimal places.) O .14 O .21 O .24 O .58 O .88 Question 4 Let A and B be two independent events. If P(A) = .4, what can you say about P(A | B)? O It is equal to .16. O It is equal to .4. O Cannot find it since P(A and B) is not known. O Cannot find it since P(B) is not known. O Cannot find it since P(A and B) both and P(B) are not known. Question 5 Dogs are inbred for such desirable characteristics as color; but an unfortunate by-product of such inbreeding can be the emergence of characteristics such as deafness. A 1992 study of bull terriers (by Strain and others, as reported in The Veterinary Journal) found the following: (i) 50% of the studied bull terriers are white. (ii) 11% of the studied bull terriers are deaf. (iii) 20% of the white bull terriers are deaf. Based on the results of this study is "being white" independent of "being deaf"? A. No, since .50 is not equal to .20. B. No, since .50 * .11 is not equal to .20. C. No, since .11 is not equal to .20. D. Yes, since .50 * .11 is not equal to .20. E. Yes, since .11 is not equal to .20.

Explanation / Answer

Question 1) We need to find P(W|H)

2) Given: P(W and H) = 0.35

P(H) = 0.6 , P(W) = 0.4

Thus, P(W|H) = P( W and H)/P(H) = 0.35/.6 = 0.58

3) P(H|W) = P(W and H)/P(W) = 0.35/0.40 = 0.88

4)Since, A and B are independent, P(A|B) = P(A) = 0.4

5) For "being white" and "being deaf" to be independent,

P(being deaf|being white) should be equal to P(being deaf)

But here, P(deaf|white) = 0.2

P(deaf) = 0.11

Thus, they are not independent since 0.11 is not equal to 0.20

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