Question 42

Mathematics Probability Medium

If a fair coin is tossed \(n\) times, then the probability that the head comes odd numbers of times is

(A) \(\frac{1}{2}\)
(B) \(\frac{1}{2^{n}}\)
(C) \(\frac{1}{2^{n-1}}\)
(D) None of these
View Dynamic Solution & Explanation
Correct Solution: Option A

Step-by-step Solution:

Total number of cases \(=2^{n}\) Number of cases when head comes odd numbers of times \(={ }^{n} C_{1}+{ }^{n} C_{3}+{ }^{n} C_{5}+\ldots=2^{n-1}\) \[\] Required probability \(=\frac{2^{n-1}}{2^{n}}=\frac{1}{2}\). \[\] Choice (a)\[\]