19 8 2. A Gallop poll askedAmericans whether they planned to watch the Super Bow
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19 8 2. A Gallop poll askedAmericans whether they planned to watch the Super Bowl. The pollster also asked those who planned to watch whether they were looking forward more to seeing the football game or the commercials. The results are summarized in the table: Gender Game Commercials Won't Watch MaleFemale 640 200 95 500 150 400 Super Bow What is the probability that a randomly selected responder was a female and watched more for the commercials? ANS: b. What is the probability that a randomly selected responder was female or watched more for the commercials? ANS:Explanation / Answer
a) Probability that a randomly selected responder was a female and watched more for commercials is computed as:
= Number of females who watched more for commercials / Total frequency
= 150 / 1985
= 0.0756
Therefore 0.0756 is the required probability here.
b) Total females = 1050 and Total commercials watching = 200 + 150 = 350
Probability that a randomly selected responder was a female or watched more for commercials is computed as:
= ( 1050 + 350 - 150) / 1985
= 1250 / 1985
= 0.6297
Therefore 0.6297 is the required probability here.
c) Given that the responder is female, probability that she watched more for the commercials is computed using the Bayes theorem as:
= Number of females who watched more for commercials / Total number of females
= 150 / 1050
= 0.1429
Therefore 0.1429 is the required probability here.
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