Question

Ten cards numbered from $1$ to $10$ are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than $3$, then the probability that it is an even number is :

• A. $\frac{4}{9}$
• B. $\frac{4}{5}$
• C. $\frac{4}{7}$
• D. $\frac{5}{7}$

Answer 1

The correct option is C $\frac{4}{7}$

Let $A$ be the event 'the number on the card drawn is even' and $B$ be the event 'the number on the card drawn is greater than $3$'.
Now the sample space of the experiment is $S=\{1,2,3,4,5,6,7,8,9,10\}$
Then $A=\{2,4,6,8,10\},B=\{4,5,6,7,8,9,10\}$
and $A\cap B=\{4,6,8,10\}$
Also $P\left(A\right)=\frac{5}{10},P\left(B\right)=\frac{7}{10}$ and $P(A\cap B)=\frac{4}{10}$
Then $P\left(A/B\right)=\frac{P(A\cap B)}{P\left(B\right)}=\frac{\frac{4}{10}}{\frac{7}{10}}=\frac{4}{7}$