Ex.15.1 Q7 Probability Solution - NCERT Maths Class 10

Go back to  'Ex.15.1'

Question

It is given that in a group of \(3\) students, the probability of \(2\) students not having the same birthday is \(0.992.\) What is the probability that the \(2\) students have the same birthday?

   

Text Solution

What is known?

It is given that in a group of \(3\) students, the probability of \(2\)  students not having the same birthday is \(0.992.\)

What is unknown?

The probability that the \(2\) students have the same birthday.

Rasoning:

This question is straight forward. We know that the sum of two complementary events are \(P\,(E) + P \) (not \(E\)\(=1.\)

By putting the given values in the above equation, we can find out the probability of not happening of event.

Steps:

Probability that \(2\) students not having the same birthday \( P\) (not \(E\)\(= 0.992\)

Probability that \(2\) students having the same birthday

\[\begin{align}P(E)&=1-0.992 \\& =0.008 \\\end{align}\]

Thus, the probability that the \(2\) students have the same birthday is \(0.008\)