Question

4) Ram & Rahim are friends, what is the probability that both will have a) different
birthdays? b) the same birthday (ignoring a leap year)?​

Answer 1

so total days = 365

favourable days = 1

so probability

= $\frac{1}{356}$

probability of not

= $\frac{365 - 1}{356}$

= $\frac{364}{365}$

Answer 2

Given:

Ram & Rahim are friends

To find:

The probability that both will have

a) different  birthdays?

b) the same birthday (ignoring a leap year)?​

Solution:

prob(event happening)

= Number of ways it can happen /Number of possible events .

prob(n people have different birthdays)

= 365 /365  × 364 /365  × 363 /365 ... × (366 − n) /365

it can be written as

= 365! /365^n(365 − n)!.

a) Therefore, the probability that both will have different  birthdays

prob(2 people have different birthdays) = 365 /365  × 364 /365  

≈ 0.997

b) The probability that both will have same  birthday (ignoring a leap year)

= 1/365