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Three coins are tossed once Find the probability of getting (i) 3 heads (ii) 2 heads (iii) at least 2 heads (iv) at most 2 heads (v) no head (vi) 3 tails (vii) exactly two tails (viii) no tail (ix) at most two tails

Solution
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When three coins are tossed once the sample space is given by
S=HHH,HHT,HTH,THH,HTT,THT,TTH,TTT
Accordingly n(S)=8
It is known that the probability of an event A is given by
P(A)= NumberofoutcomesfavourabletoATotalnumberofpossibleoutcomes=n(A)n(S)
(i) Let B be the event of the occurrence of 3 heads Accordingly B=HHH
P(B)=n(B)n(S)=18
(ii) Let C be the event of the occurrence of 2 heads Accordingly C=HHT,HTH,THH
P(C)=n(C)n(S)=38
(iii) Let D be the event of the occurrence of at least 2 heads
Accordingly D=HHH,HHT,HTH,THH
P(D)=n(D)n(S)=48=12
(iv) Let E be the event of the occurrence of at most 2 heads
Accordingly E=HHT,HTH,THH,HTT,THT,TTH,TTT
P(E)=n(E)n(S)=78
(v) Let F be the event of the occurrence of no head
Accordingly F=TTT
P(F)=n(F)n(S)=18
(vi) Let G be the event of the occurrence of 3 tails
Accordingly G=TTT
P(G)=n(G)n(S)=18
(vii) Let H be the event of the occurrence of exactly 2 tails
Accordingly H=HTT,THT,TTH
P(H)=n(H)n(S)=38
(viii) Let I be the event of the occurrence of no tail
Accordingly I=HHH
P(I)=n(I)n(S)=18
(ix) Let J be the event of the occurrence of at most 2 tails
Accordingly I=HHH,HHT,HTH,THH,HTT,THT,TTH
P(J)=n(J)n(S)=78

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