Three coins are tossed once. Fmd the probability of getting (i) 3 heads (ii) 2 heads (iii) atleast 2 heads (iv) atmost 2 heads (v) no head (vi) 3 tails (vii) exactly two tails (vm) no tail (ix) atmost two tails

Answer

N/a

Explanation

In a throw of three coins
Sample space `S={HHH,HHT,HTH,THH,H"TT",`
`THT,"TT"H,"TTT"}`
`impliesn(S)=8`
(i) Let `A=` event of getting three heads `={HHH}`
`implies n(A)=1`
`:.P(A)=(n(A))/(n(S))=1/8`
(ii) Let `B=` event of getting 2 heads
`={HHT,HTH,THH}` ltrbgt `impliesn(B)=3`
`:.P(B)=(n(B))/(n(S))=3/8`
(iii) Let `C=` event of getting atleast 2 heads
`={HHT,HTH,THH,HHH}`
`impliesn(C)=4`
`:.P(C)=(n(C))/(n(S))=4/8=1/2`
(iv) let `D=` event of getting at most 2 heads
`={HHT,HTH,THH,H"TT",THT,"TT"H,"TTT"}` ,
`impliesn(D)=7`
`:.P(D)=(n(D))/(n(S))=7/8`
(v) Let `E=` event of getting no head `={"TTT"}`
`implies n(E)=1`
`:.P(E)=(n(E))/(n(S))=1/8`
(vi) Let `F=` event of getting 3 tails `={"TTT"}`
`implies n(F)=1`
`:.P(F)=(n(F))/(n(S))=1/8`
(vii) Let `G=` event of getting exactly 2 tails
`={H"TT",THT,"TT"H}`
`=n(G)=3`
`:.P(G)=(n(G))/(n(S))=3/8`
(vii) Let `H=` event of getting no tails
`={HHH}`
`implies n(H)=1`
`:.P(H)=(n(H))/(n(S))=1/8`
(ix) Let `I=` event of getting atmost 2 tails
`={HHH,HHT,HTH,THH,H"TT",THT,"TT"H}`
`impliesn(I)=7`
`:.P(I)=(n(I))/(n(S))=7/8`