If two coins are tossed simultaneously, then find the probability of the following events: (a) at least one tail turns up. (b) no head turns up. (c) at the most one tail turns up.

If two coins are tossed simultaneously, then find the probability of the following events:

(a) at least one tail turns up.  (b) no head turns up.  (c) at the most one tail turns up.

Answer: Since two coins are tossed simultaneously

{ H H Sample Space is = H T T H T T }

∴ n(S) = 4

(a) Let A = Event that at least one tail turns up

A = {HT,  TH,  TT}

n(A) = 3

∴ P(A) = n(A) n(S) ∴ P(A) =    3    4

(b) Let B = Event of getting no  head turns up

∴ B = {HH}

∴ n(B) = 1

∴ P(B) = n(B) n(S) ∴ P(B) =    1    4

(c) Let C = Event of getting at the most one tail turns up

C = {HH, TH, HT}

n(C) = 3

∴ P(C) = n(A) n(S) ∴ P(C) =    3    4