In a hostel, $60 \%$ of the students read Hindi newspaper, $40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. A student is selected at random.(i) Find the probability that he reads neither Hindi nor English news paper.(ii) If he reads Hindi newspaper, what is the probability that he reads English newspaper?

Home » In a hostel, of the students read Hindi newspaper, read English newspaper and read both Hindi and English newspapers. A student is selected at random.(i) Find the probability that he reads neither Hindi nor English news paper.(ii) If he reads Hindi newspaper, what is the probability that he reads English newspaper?

In a hostel, $60 \%$ of the students read Hindi newspaper, $40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. A student is selected at random.
(i) Find the probability that he reads neither Hindi nor English news paper.
(ii) If he reads Hindi newspaper, what is the probability that he reads English newspaper?

In a hostel, $60 \%$ of the students read Hindi newspaper, $40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. A student is selected at random.
(i) Find the probability that he reads neither Hindi nor English news paper.
(ii) If he reads Hindi newspaper, what is the probability that he reads English newspaper?

Let $\mathrm{P}(\mathrm{A})$ be the probability of students reading Hindi newspaper.
$\therefore P(A)=0.60$
Let $\mathrm{P}(\mathrm{B})$ be the probability of them reading English newspaper.
$\therefore P(B)=0.40$
Let $\mathrm{P}(\mathrm{A} \cap \mathrm{B})$ be the probability them reading both.
$\therefore \mathrm{P}(\mathrm{A} \cap \mathrm{B})=0.20$
Let $P(A \cup B)$ be the probability them reading either one of them.
$\begin{array}{l} \therefore P(A \cup B) \\ =P(A)+P(B)-P(A \cap B) \\ =0.60+0.40-0.20 \\ =0.80 \end{array}$
(i)The probability that none of them reads either of them
$\begin{array}{l} =1-0.8 \\ =0.2 \\ =1 / 5 \end{array}$
(ii)The probability that he reads the English one given that he reads the Hindi one:
$\begin{array}{l} P(A / B) \\ =\frac{P(A \cap B)}{P(A)} \\ =\frac{0.20}{0.60} \\ =\frac{1}{3} \end{array}$