Question

The probability that Chahri passes in mathematics is $\dfrac{2}{3}$ and probability that he passes in English is $\dfrac{4}{9}$ . If the probability of passing both course is $\dfrac{1}{4}$ , then the probability that Chahri will pass in at least one of the subject is $\dfrac{{31}}{{36}}$ .

Answer 1

Hint: We will first write the event then, for finding the probability we use P(A∪B) = P(A) + P(B) –P(A∩B)

Complete step-by-step answer:
Let A be the event that Chahri passes in mathematics and B be the event that he passes in English.
We have, $P(A) = \dfrac{2}{3}$
$P(B) = \dfrac{4}{9}$
P (getting pass in both course) = P (A∩B)$ = \dfrac{1}{4}$
∴ Probability that Chahri pass in at least one subject is
= P (A∪B) = P (A) + P (B) – P (A∩B)
=$\dfrac{2}{3} + \dfrac{4}{9} - \dfrac{1}{4}$
$ = \dfrac{{31}}{{36}}$
So, the above option is true.

Note: In this type of question, first represent events by different letters. It is recommended that first try to write all the events and outcomes then, we can proceed as per question asked.