A balanced coin is tossed four times List the possible outco

A balanced coin is tossed four times. List the possible outcomes and compute the probability of each of the three events:
(a) exactly three heads
(b) at least one head
(c) the number of heads equals the number of tails
(d) the number of heads exceeds the number of tails

Solution

A balanced coin is tossed four times, So the possible outcomes can be following:

possible outcomes are 2 and trials are 4

Sample space is determined by= 2⁴=16

HHHH HTHH THHH HTHT

HHHT HTTH TTHH THTH

HHTT HHTH TTTH THHT

HTTT TTTT TTHT THTT

These are 16 sample points.

a) Probability of exactly three heads= no. of outcomes containing exactly three H/ Total outcomes= 4/16

b) Probability of At least one head= 1- Probabolity of no head= 1- (No. of outcomes cotaining no head/ total outcomes)= 1-1/16=15/16

c) Probability of that the no. of heads equals the no. of tails= No. of outcomes containing two H and two T/ Toal outcomes= 6/16

d) Probability of that the no. of heads exceeds the no. of tails= No. of outcomes cotaining H more than T/ Total outcomes = 4/16