Question

A fair coin is tossed four times. What is the probability that the number of heads appearing on the first two tosses is equal to the number of heads appearing on the second two tosses

Answer 1

Answer: 3/8

Explanation:

Since it is a fair coin, then generally, P(Head) = P(Tail) = ½

And since we've been asked to find the probability that the number of heads in the first two tosses be equal to the number of heads in the second two tosses, tossing a fair coin four times, the possible outcomes of having equal number of heads in first two tosses and second two tosses becomes:

[HHHH] or [HTHT] or [THTH] or [TTTT] or [HTTH] or [THHT]

=[½*½×½*½] + [½*½×½*½] + [½*½×½*½] + [½*½×½*½] + [½*½×½*½] + [½*½×½*½]

=1/16 * 6

=6/16

=3/8.