2. A coin is tossed three times then find the probability of
(i) getting head on middle coin
(ii) getting exactly one tail
(iii) getting no tail
Sol. When a coin tossed three times
S = { HHH, HTH, THH, TTH, HHT, HTT, THT, TTT }
n (S) = 8
(i) Let A be the event of getting head on middle coin
A = { HHH, THH, HHT, THT }
n (A) = 4
P (A) = n (A)/n (S)
∴ P (A) = 4/8
∴ P (A) = 1/2
(ii) Let B be the event of getting exactly one tail
B = { HTH, THH, HHT }
n (B) = 3
P (B) = n (B)/n (S)
∴ P (B) = 3/8
(iii)Let C be the event of getting no tail
C = { HHH }
n (C) = 1
P (C) = n (C)/n (S)
∴ P (C) = 1/8
