In a hostel,60 % of the students read Hindi n | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $H$ denote the set of students who read Hindi newspaper and $E$ denote the set of students who read English newspaper.Given that:$P(H) = 60 \%

Vedclass · Accepted Answer

$1/5$

Vedclass · Answer

(A) Let $H$ denote the set of students who read Hindi newspaper and $E$ denote the set of students who read English newspaper.Given that:$P(H) = 60 \% = 0.60$$P(E) = 40 \% = 0.40$$P(H \cap E) = 20 \% = 0.20$The probability that a student reads at least one of the two newspapers is given by the addition theorem:$P(H \cup E) = P(H) + P(E) - P(H \cap E)$$P(H \cup E) = 0.60 + 0.40 - 0.20 = 0.80$The probability that a student reads neither Hindi nor English newspaper is the complement of $P(H \cup E)$:$P((H \cup E)') = 1 - P(H \cup E)$$P((H \cup E)') = 1 - 0.80 = 0.20$Converting to fraction:$0.20 = \frac{20}{100} = \frac{1}{5}$

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. Find the probability that she reads neither Hindi nor English newspapers.

Similar Questions

The sum of all the elements of the set $\{\alpha \in \{1, 2, \ldots, 100\} : \operatorname{HCF}(\alpha, 24) = 1\}$ is

In a group of $70$ people,$37$ like coffee,$52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

In a survey of $600$ students in a school,$150$ students were found to be taking tea and $225$ taking coffee,$100$ were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

The probability that at least one of the events $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.2$,then $P(A') + P(B')$ is equal to

Out of $500$ car owners investigated,$400$ owned car $A$ and $200$ owned car $B$,and $50$ owned both car $A$ and car $B$. Is this data correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module