Question

$12$ cards, numbered $1$ to $12$, are placed in a box, mixed up thoroughly and then a card is drawn at random from the box. If it is known that the number on the drawn card is more than $3$, find the probability that it is an even number.

Answer 1

Let A and B be the events of "The number on the card drawn is even" and "the number on the card is greater than $3$"

Therefore,

$s=1,2,3,4,5,6,7,8,9,10,11,12$

$A=2,4,6,8,10,12$ and

$B=4,5,6,7,8,9,10,11,12$

and $(A\cap B)=4,6,8,10,12$

$p\left(A\right)=\frac{6}{12},p\left(B\right)=\frac{9}{12}$

and $P(A\cap B)=\frac{5}{12}$

so he required probablity is:

$P\left(\frac{A}{B}\right)=\frac{P(A\cap B)}{P\left(B\right)}$

$=\frac{5}{12}\times \frac{12}{9}$

$=\frac{5}{9}$

This is the right solution.