In a class, $40 \%$ students study mathematics; $25 \%$ study biology and $15 \%$ study both mathematics and biology. One student is selected at random. Find the probability that(i) he studies mathematics if it is known that he studies biology(ii) he studies biology if it is known that he studies mathematics.

Home » In a class, students study mathematics; study biology and study both mathematics and biology. One student is selected at random. Find the probability that(i) he studies mathematics if it is known that he studies biology(ii) he studies biology if it is known that he studies mathematics.

In a class, $40 \%$ students study mathematics; $25 \%$ study biology and $15 \%$ study both mathematics and biology. One student is selected at random. Find the probability that
(i) he studies mathematics if it is known that he studies biology
(ii) he studies biology if it is known that he studies mathematics.

In a class, $40 \%$ students study mathematics; $25 \%$ study biology and $15 \%$ study both mathematics and biology. One student is selected at random. Find the probability that
(i) he studies mathematics if it is known that he studies biology
(ii) he studies biology if it is known that he studies mathematics.

Let $\mathrm{P}(\mathrm{A})$ be the probability of students studying mathematics.
$\therefore P(A)=0.40$
Let $\mathrm{P}(\mathrm{B})$ be the probability of students studying biology.
$\therefore P(B)=0.25$
Let $\mathrm{P}(\mathrm{A} \cap \mathrm{B})$ be the probability of students studying both mathematics and biology.
$\therefore P(A \cap B)=0.15$
One student is selected at random.
(i) The probability that he studies mathematics given that he studies biology:
$\begin{array}{l} P(A / B) \\ =\frac{P(A \cap B)}{P(B)} \\ =\frac{0.15}{0.25} \\ =\frac{3}{5} \end{array}$
(ii) The probability that he studies biology given that he studies mathematics:
$\begin{array}{l} \mathrm{P}(\mathrm{A} / \mathrm{B}) \\ =\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{B})} \\ =\frac{0.15}{0.40} \\ =\frac{3}{8} \end{array}$