31. Three coins are tossed once. Find 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
(viii) No tail
(ix) Atmost two tails
31. Three coins are tossed once. Find 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
(viii) No tail
(ix) Atmost two tails
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1 Answer
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31. When three coins are tosses we have the sample space,
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
So, n (S) = 8
(i) Let A: 3 heads occurs.
A = {HHH}
So, n (A) = 1
? P (A) =
(ii) Let B: 2 heads occurs
B = {HHT, HTH, THH}
So, n (B) = 3
? P (B) =
(iii) Let C: at least 2 heads occurs i.e. 2 heads or more
C = {HHT, HTH, THH, HHH}
So, n (C) = 4
? P (C) =
(iv) Let D: at most 2 heads occurs i.e. 2 heads or less
D = {TTT, HTT, THT, TTH, HHT, HTH, THH}
So, n (D) = 7
? P (D) =
(v) Let E: no head occurs
E = {TTT}
So, n (E) = 1
? P (E) =
(vi) Let F: 3 tails occurs
F = {TTT}
So, n (F) = 1
? P (F) =
(vii) Let G: exactly two tail
...more
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