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

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