Question

An unbiased coin is tossed thrice. What is the probability of receiving more heads than tails is ?​

Answer 1

$\huge\b{Answer:}}$

$\large\bold{\frac{1}{2}}$.

$\huge\b{Explanation:}}$

P(at least 2 heads) ,

= P(2 heads OR 3 heads) ,

= P(2 heads) + P(3 heads),

=$\large\bold{\frac{3}{2}*\frac{1}{8}+\frac{3}{3}*\frac{1}{8}}$,

= 3/8 + 1/8 ,

= 4/8 ,

= 1/2 .

Alternatively:

By symmetry, P(at least 2 heads) = P(at least 2 tails) ,

But these events partition the sample space of all possible outcomes, so

P(at least 2 heads) + P(at least 2 tails) = 1 ,

=> 2 × P(at least 2 heads) = 1 ,

=> P(at least 2 heads) = 1/2.