Question

Hira and Sarita are friends. What is the probability that both will have –
I.Different birthdays?
II.The same birthday?

Answer 1

Hint : The term probability defines the term probable, the event which is likely to happen. Here we will use the definition of the probability which can be defined as the ratio of the favorable outcomes upon the total possible outcomes.

Complete step-by-step answer :
I.Here any non-leap year has total $365$ days, therefore the total possible outcomes here will be $n = 365$
If both Sarita and Hamida were born on different days.
Let us assume that “A” is the event when both Sarita and Hamida were born on different day.
$n(A) = 364$
Now, the required probability can be given by –
$P(A) = \dfrac{{n(A)}}{n}$
Place the values in the above expression –
$P(A) = \dfrac{{364}}{{365}}$ ….. (A)

II.If both Sarita and Hamida were born on the same day
Let us assume that “B” be the event when both Sarita and Hamida were born on the same day.
$n(B) = 1$
Now, the required probability can be given by –
$P(B) = \dfrac{{n(B)}}{n}$
Place the values in the above expression –
$P(B) = \dfrac{1}{{365}}$ ….. (B)
Hence, the equations (A) and (B) are the required solution.

Note : Always remember that the probability of any event lies between zero and one. If the probability is expressed in the form of fraction, then the denominator is always bigger than the numerator. The probability of the sure event is always one and impossible event is always zero.