Calculating the probability that in a class of 20 students, there are at least two with...

Calculating the probability that in a class of 20 students, there are at least two with the same birthday.

(a) First, calculate the probability that each student has a different birthday as follows (round to four decimal places)

b) Explain briefly why the above probability is calculated that way.

(c) Now note that the probability that there are at least two with the same birthday is the complement of the above probability. What is the probability that there are at least two with the same birthday

Solutions

Expert Solution

solution:

total students = 20

number of days in a year = 365

a) so probability that all students have the different birthday =

where n = total possible choices

r = favourable choices

so probability that all students have the different birthday =

b) we have to find that atleast 2 students have the same birthday.

so we know that the total probability always equal to 1. and if the probability of all students have the different birthday is deducted by the total probability , we can get the atleast two students have the same birthday

c) so from the b we can said that the above (a) probability is the complimentary of the required probability

so, so probability that atleast two students have the same birthday = 1 - P(all with different birthday)

so probability that atleast two students have the same birthday = 1 - 0.5886 = 0.4114

orchestra answered 1 year ago

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