assume that there are 365 days in a year, the probability that a person is born on any given day is the same for all days, and everyone’s birthdays are independent.
(a) if there are n people, what is the probability that no one is born in july?
(b) if there are 15 people who are all born in july or august, what is the probability that at least two of these people share the same birthday?
for part a, wouldn't it just be 365^n - 365^31 since there are only 31 days in july? is there a way to make it more order specific? for b i am still confused on how to make order matter if we are just taking days from july or august. explanations well appreciated!

Step-by-step explanation:

If each day equal chance then p = Prob that a person is borne on a particular day = 1/365

Each person is independent of the other and there are two outcomes either borne in July or not

p = prob for one person not borne in July = (365-31)/365 = 334/365

a)Hence prob that no one from n people borne in July =

b) p = prob of any one borne in July or Aug = =0.1698

X- no of people borne in July or Aug

n =15

P(X>=2) =

=0.7505

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the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.