Question

# 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 2 tails (viii) no tail (ix) at most two tails.

Solution

## Here three coins are tossed once. The sample space S is S={HHH,HHT,HTH,THH,TTH,THT,HTT,TTT} ∴ n(S) = 8  (i) Let A be the event of getting 3 heads. A = {HHH}  ∴n(A)=1 Thus P(A)=n(A)n(S)=18 (ii) Let B be the event of getting 2 heads. B = {HHT, HTH, THH,} ⇒n(B)=3  Thus P (B) =N(B)n(S)=38  (iii) Let C be the event of getting at least 2 heads. C = {HHH, HHT, HTH, THH} ⇒n(C)=4  Thus P(C) =n(C)n(S)=48=12  (iv) Let D be the event of getting at most 2 heads. D = {HHT, HTH, THH, TTH,THT, HTT, TTT} ⇒n(D)=7 Thus P(D)=n(D)n(S)=78.(v)Let E be the event of getting no head.E=TTT⇒n(E)=1Thus P(E)=n(E)n(S)=18(vi) Let F be the event of getting 3 tails.F{TTT}⇒n(F)=1Thus P(F)=n(F)n(S)=18(vii) Let G be the event of getting exactly two tails.G={TTH,THT,HTT}⇒n(G)=3Thus P (G) = n(G)n(S)=38(viii) Let K be the event of getting no tail.K={HHH}⇒n(K)=1Thus P(K)=n(K)n(S)=18.(xi) Let L be the event of getting at most two tailsL={HHH,TTh,THT,HTT,HHT,HTH,THH}⇒n(L)=7Thus P(L)=n(L)n(S)=78

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