MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
A fair coin is tossed five times in succession. Define the following events:
A = "the first toss results in a head",
B = "the last toss results in a tail".
(i) Verify, by direct computation, that events A and B are independent.
(ii) Using your result from part (i), find the probability that both A and B occur in a single sequence of five tosses.
(iii) Suppose the entire experiment of five tosses is repeated independently 100 times. Find the expected number of sequences in which both A and B occur together.