Suppose there are 50 students in our class. What\'s the probability that there a

Question

Suppose there are 50 students in our class. What's the probability that there are at least two of them having the same birthday? Assume the birthdays of people are randomly distributed among 365 days of a year. In a particular market, there are three hotels available. Research shows that 30% of patrons choose hotel A. 55% choose hotel B, and 15% choose hotel C. (Note that, in this context, hotel choices are mutually exclusive and every patron in this market must choose exactly one of these three hotels.) Of patrons who stay at hotel A, 15% stay in rooms that are in need of repair; of patrons who stay at hotel B. 25% stay in rooms that are in need of repair; and, of patrons who stay at hotel C. 25% stay in rooms that are in need of repair. Suppose that a patron who stayed at a hotel in this market is selected at random. What is the probability that the patron stayed in a room that was in need of repair?

Explanation / Answer

3) probabilty that at least 2 people share their b'th day=1-P(none of them share birthday)

=1-(first one has 365 choices for birth day, 2nd 364, 3rd 363,....50th (365-51))

=1-(365/365 *364/365 *363/365*........*(365-51)/365)

=1-0.0296=0.9704

4) probabilty of choosing hotel A=P(A)=0.30 ; hotel B =P(B)=0.55 ;hotel C =P(C) =0.15

room need to be repaired given hotel A =P(R|A) =0.15

room need to be repaired given hotel B =P(R|B) =0.25

room need to be repaired given hotel C =P(R|C) =0.25

therefore probability that room needs to be repaired =P(R) =P(A)*P(R|A)+P(B)*P(R|B)+P(C)*P(R|C)

=0.3*0.15+0.55*0.25+0.15*0.25=0.22

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