NCERT Class X Chapter 14: Probability Example 6

NCERT Class X Chapter 14: Probability Example 6

Question:

Savita and Hamida are friends. What is the probability that both will have (i) different birthdays? (ii) the same birthday? (Ignoring a leap year).

Given:

Two friends, Savita and Hamida.

To Find:

(i) Probability that both have different birthdays.
(ii) Probability that both have the same birthday.

Formula:

Probability = Favorable Outcomes Total Outcomes

Solution:

(i) Probability of different birthdays:

Total number of days in a year = 365

Let Savita's birthday be on any day. 

The probability that Hamida's birthday is different from Savita's is 365-1 365

The probability that Hamida's birthday is different from Savita's is \( \frac{364}{365}\)

(ii) Probability of same birthdays:

Total number of days in a year = 365

The probability that Hamida's birthday is the same as Savita's is 1 365

Result:

(i) Probability that both have different birthdays = 364 365

(ii) Probability that both have the same birthday = 1 365

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