In a random group of 5 people what is the probability that a

In a random group of 5 people what is the probability that at teast 2 people were born in the same month? (assume that all months have the same member of days) 0.588 0.598 0.608 0.618 0.628 Assume that 25% of the comadian population is considered to be over weight. IF 4 people are selected at random, what is the probability that exactly 1.9 them is over weight? .222 .322 .422 .522 .622

Solution

(a)no. of ways of arranging months with 5 persons = 12⁵

no one same month = ¹²P₅

so probability of no one in same month = ¹²P₅/12⁵ = 0.3819444444444444

so probability of any 2 persons in same month = 1-0.3819444444444444 = 0.618

so (C)

(b)

let the population be 4N

so of 4N, 4 are selected no. of ways = ^4NC₄

of this 1 is overweight so no. of ways = ^3NC₃*^NC₁

so probabily = 3³/4⁴*4!/3! = 27/64 = 0.421875 by taking N-->inf

or probability = 0.422