a fair coin is tossed four times and the sequences of heads

a fair coin is tossed four times, and the sequences of heads and tails is observed. List each of the 16 sequences in the sample space S. Let events A, B, C, and D be given by A, B, C, and D. If the probability set function assigns 1/16 to each outcome in the sample space, find (i)P (A), (ii)

Solution

List of 16 sequences is shown below:

H H H H
H H H T
H H T H
H H T T
H T H H
H T H T
H T T H
H T T T
T H H H
T H H T
T H T H
T H T T
T T H H
T T H T
T T T H
T T T T

events A, B, C, and D be givenby:

A={at least 3heads}, B={at most 2 heads), C={ heads on the third toss},D={1 head and 3 tails}

out of given 16 sequences, 5 sequences (HHHH, HHHT, HHTH, HTHH, THHH) have at least 3 heads. therefore:

P(A) = 5/16