Let Ajay will not appear in JEE exam with probability p=2/7, while both Ajay and Vijay will appear in the exam with probability q=1/5. Then the probability, that Ajay will appear in the exam and Vijay will not appear is :

Solution

Maths sir · 3 steps

Ajay appearing splits into two cases, with Vijay and without him, so subtract the 'both' part.

1. Name the events. Let A be 'Ajay appears' and V be 'Vijay appears'. The given p = 2/7 is the chance that Ajay does not appear, so P(A) = 1 - 2/7 = 5/7.
2. Split Ajay's event. Whenever Ajay appears, Vijay either appears too or does not. These two cases cannot happen together, so their probabilities add up to P(A).

   P(A ∩ V̄) = P(A) - P(A ∩ V) = 5/7 - 1/5

3. So. 5/7 - 1/5 = 25/35 - 7/35 = 18/35, which is option (d).

The idea to keep. For 'A happens but B does not', use P(A ∩ B̄) = P(A) - P(A ∩ B). Always check whether the given probability is for an event or for its complement.

Answer from the NTA final answer key. Solution by PrepWiser.