Question: Assertion (A): Two coins are tossed simultaneously.the probability of getting two heads,if is known that at one least one head comes up,is 1/3 Reason (R): let E and F be two event with a random experiment,then p(F/E)=p(E^F)/P(E).
The correct answer is –
Assertion (A) states that the probability of getting two heads when two coins are tossed simultaneously and at least one head comes up is 1/3.
Reason (R) states that if E and F are two events in a random experiment, then the conditional probability of F given E is equal to the probability of the intersection of E and F divided by the probability of E.
The reason is a general rule for conditional probability and is correct. However, it is not directly related to the assertion.
To find the probability of getting two heads when at least one head comes up, we can use the formula for conditional probability:
P(A/B) = P(A and B) / P(B)
Here, let A be the event of getting two heads and B be the event of getting at least one head. Then, we have:
P(A and B) = P(A) = 1/4, since there is only one way to get two heads out of four possible outcomes when two coins are tossed.
P(B) = 3/4, since there are three possible outcomes out of four when at least one head comes up (HH, HT, TH).
Therefore, the conditional probability of getting two heads given that at least one head comes up is:
P(A/B) = P(A and B) / P(B) = (1/4) / (3/4) = 1/3
So, the assertion is true and the reason is also true, but the reason does not explain or justify the assertion. Hence, the correct option is (A).
