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Answer 1 · 2015-09-27T11:25:12

Muhammad K. - First find the probability that all 3 outcomes are the same.

P(all heads) = $(1/2)^3 = 1/8$

P(all tails) = $(1/2)^3 = 1/8$

P(all outcomes the same) = $1/8+1/8 = 1/4$

Geometric Distribution :

(a) P(exactly three rounds of flips are needed for the 1st success) =

$(1-1/4)^2(1/4)$ = $9/64$

(b) P(more than 4 flips are needed for the 1st success) = $1 - P(X <=4)$

$= 1 - [(1/4) + (1-1/4)^1(1/4) + (1-1/4)^2(1/4)+ (1-1/4)^3(1/4)]$

= $1 - 175/256$ = $81/256$

Hope that helped