ponucar aaion P.5* Before the 2009 Super Bowl there was a coin flip to determine
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ponucar aaion P.5* Before the 2009 Super Bowl there was a coin flip to determine who kicked off and who received. The NFC (National Football Conference) had won 11 prior coin flips. (a) Given that the NFC had won 11 straight flips, what is the probability that they would win the 12th flip? Explain. (b) Before the 2010 Super Bowl (won by the New Orleans Saints) the NFC won the coin toss for the 13th consecutive time. What is the probability that the NFC will win the next two consecutive tosses? P6 At supermarkets in a Midwestern city the sales of canned tuna varies from week to week. Marketing researchers have determined that there is a relationship between sales of canned-tuna and the price of canned tuna. Specifically, SALES = 40710 430PRICE where SALES are cans sold per week and PRICE is measured in cents per can. Suppose PRICE over the year can be considered (approximately) a normal random variable with mean 75 cents and standard deviation = 5 cents. That is PRICE N(75, 25) (a) What is the numerical expected value of SALES? Show your work. (b) What is the numerical value of the variance of SALES? Show your work. (c) Find the probability that more than 6,300 cans are sold in a week. Draw a sketch illustrating the calculation.Explanation / Answer
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P . 5 Assuming the coin is fair and unbiased,
As the coin flips are independent of each other, the probability of coin landing as heads or tails on ith flip is independent of any other flip and hence, probability of anyone winning a toss on a particular flip is 0.5 irrespective of any other flip.
Hence,
(a) P(winning the 12th flip) = 0.5
(b) P(winning the next 2 flips) = 0.5*0.5 = 0.25
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