1.

Three fair coins are tossed together. Find the probability of getting(i) all heads(ii) atleast one tail(iii) atmost one head(iv) atmost two tails

Answer»

Three fair coins are tossed together

Sample spade = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

n(S) = 8

(i) Let A be the event of getting all heads

A = {HHH}

n(A) = 1

P(A) = \(\frac{n(A)}{n(S)}=\frac{1}{8}\)

(ii) Let B be the event of getting atleast one tail.

B = {HHT, HTH, HTT, THH, THT, TTH, TTT}

n(B) = 7

P(B) = \(\frac{n(B)}{n(S)}=\frac{7}{8}\)

(iii) Let C be the event of getting atmost one head

C = {HTT, THT, TTH, TTT}

n(C) = 4

P(C) = \(\frac{n(C)}{n(S)}=\frac{4}{8}=\frac{1}{2}\)

(iv) Let D be the event of getting atmost two tails.

D = {HTT, TTT, TTH, THT, THH, HHT, HTH}

n(D) = 7

P(D) = \(\frac{n(D)}{n(S)}=\frac{7}{8}\)


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