A biased coin shows Head with probability on every toss
MATHEMATICS · Subjective · CBSE · Mathematics · Probability · Probability
Problem
A biased coin shows Head with probability p on every toss, where 0<p<1. The coin is tossed three times. Define the events
A : “exactly two Heads occur”,
B : “the first toss is Tail”.
Answer the following questions.
(i) Express P(A) and P(B) in terms of p.
(ii) Obtain P(A∩B) in terms of p.
(iii) Find all value(s) of p for which events A and B are independent.
(iv) Investigate whether events A and B can ever be mutually exclusive. Provide full reasoning.