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Mathematics · Probability · NCERT Examples

Example 6

A complete, independently verified solution for NCERT Example 6.

Mathematics · Chapter 14 · NCERT Examples

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NCERT Example

Example 6

birthdays · complementary events

Savita and Hamida are friends. Ignoring a leap year, find the probability that both have (i) different birthdays and (ii) the same birthday.

Solution

Board-exam working:

Fix Savita's birthday. Hamida's birthday can be any one of 365 equally likely days.

(i) To have a different birthday, Hamida can be born on any of the other days.

365−1=364365-1=364
P(different birthdays)=364365P(\text{different birthdays})=\frac{364}{365}

(ii) The same-birthday event is the complement of the different-birthday event.

P(same birthday)=1−364365=1365P(\text{same birthday})=1-\frac{364}{365}=\frac1{365}

Final answer

(i) 364365(ii) 1365\boxed{\text{(i) }\frac{364}{365}\qquad\text{(ii) }\frac1{365}}