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Q. Savita and Hamida are friends, what is the probability that both will

have (i) the same birthday (ii) different birthdays (ignoring a leap year).

{ (1,1),

(2,1), (2,2), (2,3), ………, 2,365),

(3,1), (3,2), (3,3), ……, (3,365),

…………

(365,1),(365,2),(365,3) ,………….., (365,365) }

(1,2),

(1,3),

………_’

(1,365),

All possible outcomes are

365 rows

365 columns

Total no. of possible outcomes = 365 x 365

…………

Let A be the event that both Savita and Hamida have their birthday on same day

∴ Number of outcomes favourable to A = 365

Let B be the event that both Savita and Hamida have their birthday on different days

Hamida’s birthday on 1^st Jan

i.e. 1^st day of year

Hamida’s birthday on 2nd Jan

i.e. 2nd day of year

Hamida’s birthday on 3rd Jan

i.e. 3rd day of year

Hamida’s birthday on 31st Dec

i.e. 365th day of year

SAME

DAY

Savita’s birthday on 2nd Jan

i.e. 2nd day of year

DIFFERENT

DAY

Hamida’s birthday on 1st Jan

i.e. 1st day of year

Hamida’s birthday on 3rd Jan

i.e. 3rd day of year

Hamida’s birthday on 2nd Jan

i.e. 2nd day of year

∴ n (B) =

365 x 365

- 365

= 365 ( )

365 - 1

∴ Number of outcomes favourable to B is 365 x 364

Since there are 365 rows ,there are 365 diagonal elements

Probability of event A is

Probability of event B is

Sol.

^{Savita’s birthday on 1st Jan}

^{i.e. 1st day of year}

No. of outcomes with birthday on different day =

Total No. of outcomes – No. of outcomes with Birthday on same day

If we observe all the elements on the diagonal , we observe that both their birthdays fall on the same day

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