Two students Anil and Ashima appeared in an e | vedclass

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

Question

(A) Let $E$ and $F$ denote the events that Anil and Ashima will qualify the examination,respectively.Given that $P(E) = 0.05$,$P(F) = 0.10$,and $P(E \

Vedclass · Accepted Answer

$0.87$

Vedclass · Answer

(A) Let $E$ and $F$ denote the events that Anil and Ashima will qualify the examination,respectively.Given that $P(E) = 0.05$,$P(F) = 0.10$,and $P(E \cap F) = 0.02$.The event 'both Anil and Ashima will not qualify the examination' is represented as $E' \cap F'$.By De Morgan's Law,$E' \cap F' = (E \cup F)'$.First,we calculate the probability that at least one of them qualifies:$P(E \cup F) = P(E) + P(F) - P(E \cap F)$$P(E \cup F) = 0.05 + 0.10 - 0.02 = 0.13$.Now,the probability that neither qualifies is:$P(E' \cap F') = P((E \cup F)') = 1 - P(E \cup F)$$P(E' \cap F') = 1 - 0.13 = 0.87$.

Similar Questions

If $A$ and $B$ are two events of a random experiment such that $P(A \cup B) = P(A \cap B)$, then which one amongst the following four options is not true?

If $P(A) = \frac{1}{2}$,$P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$,then the value of $P(A' \cap B')$ is

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is:

$A$ man and his wife appear in an interview for two vacancies. The probability of the husband's selection is $1/7$ and the probability of the wife's selection is $1/5$. What is the probability that only one of them is selected?

One die and a coin (both unbiased) are tossed simultaneously. The probability of getting $5$ on the top of the die and tail on the coin is

Vedclass Test Series

Exam Paper Generator

Online Exam Module