Anita, Sita, Gita and Rita are four friends. What . . .

Question : Anita, Sita, Gita and Rita are four friends. What is the probability that (in a non leap year)

i) All will have same birthday?

ii) Their birthdays fall in the month of October?

iii) Their birthdays fall on 10th day of the months?

iv) Their birthdays fall in January or February?

Doubt by Chesta 

Solution : 

Total number of days in a non leap year = 365

P(E) = No. of favorable outcomes / Total No. of possible outcomes

i) All of will have the same birthday, it means that all of them will have the birthday on a single day out of 365 days of leap year.

P(same birthday) = 1/365

ii) All of them have birthday in the month of October. The month of October has  31 days so their birthday could fall in any of the 31 days of 365 days. 

P(have birthday in the month of October) = 31/365

iii) Their birthday could fall on the 10th day of the month. Since there are 12 month and hence there could a total of 12 outcomes having 10th day of month. So the favorable outcomes would be 12 days.

P(have birthday on 10th day of the month) = 12/265

iv) Their birthday falls in the month of January or February. Since the month of January has 31 days & in a non leap year the month of February has 28 days so the favorable outcomes would be 31+28 = 59 days.

P(Their birthdays fall in January of February) = 59/365