# 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.

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 (i) Let B be the event of the occurrence of 3 heads. Accordingly, B = {HHH}

∴P(B) = (ii) Let C be the event of the occurrence of 2 heads. Accordingly, C = {HHT, HTH, THH}

∴P(C) = (iii) Let D be the event of the occurrence of at least 2 heads.

Accordingly, D = {HHH, HHT, HTH, THH}

∴P(D) = (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) = (v) Let F be the event of the occurrence of no head.

Accordingly, F = {TTT}

∴P(F) = (vi) Let G be the event of the occurrence of 3 tails.

Accordingly, G = {TTT}

∴P(G) = (vii) Let H be the event of the occurrence of exactly 2 tails.

Accordingly, H = {HTT, THT, TTH}

∴P(H) = (viii) Let I be the event of the occurrence of no tail.

Accordingly, I = {HHH}

∴P(I) = (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) = • 12
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