Ambikesh can either take biology or math in his class 12. If he takes biology, then he will get 'A' grade with probability 3/4 because his girlfriend is ready to teach him and if he takes math he will get 'A' grade with probability 1/3.
He decided to choose the stream by flipping the coin . What is the probability that
1. he will get 'A' in biology.
2. he will get 'A' in Maths.
To get 'A' in Biology he needs to take Biology stream first.
P(Biology)= P(Maths) = 1/2 and
P(getting 'A' / Biology) = 3/4
P(getting 'A'/ Maths) = 1/3
P(Grade 'A' ∩ Biology) = P(Biology) * P(getting 'A' / Biology) // from conditional probabilty formula
= (1/2)* (3/4 )
P(Grade 'A' ∩ Maths) = (1/2) * (1/3 )