Former Major League Baseball player Barry Bonds hit one home

Former Major League Baseball player Barry Bonds hit one home run for every 18.2 at bats at Atlanta-Fulton Stadium, but only one home run per 31.8 at bats at Shea Stadium. [Source: H. Araton, \"Selig cannot look away this time,\" The New York Times, May 29, 2007.] What\'s the probability that Bonds hit at least one home run in four at bats at each stadium? Customer-friendly banks with open floor plans, multiple entrances, and no \"bandit barriers\"-the thick, clear walls between tellers and customers-are being blamed for an increase in bank robberies. Bank robberies in six northern New Jersey counties increased from 44 in 2006 to a rate of 75 per year in 2007. (Source: C. J. Hughes, \"An increase in banks, and robberies: Customer-friendly branches are vulnerable, police say,\" The New York Times, August 12, 2007.] What\'s the probability that there will be more than eight bank robberies in northern New Jersey next month, assuming the new rate holds? You have 20 pairs of socks in your sock drawer. Eight pairs are red. You put on a blindfold, your roommate mixes the pairs of socks, and you select five pairs. What Is the probability that more than three pairs are red?

Solution

Here we calculate each probability as binomial separate and multiply both for answer as the two are independent.

p = 1/18,2 and 1/31.8

PROb for winning atleast 1 in 4 in Atlanta stadium=0.2022

PROb for winning atleast 1 in 4 in Shea stadium=0.1198

Hence for both = 0.2022(0.1198)=0.0242

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x - no of bank robbereies is Poisson with mean =75

P(X>8) = 1

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no of pairs of socks =20

red socks = 8

Prob for a red pair to be selected =8/20 =0.4

X - no of red pairs is binomial with p =0.4 and n =5

P(x>3) = 0.08704