Question #05ff8

1 Answer
Sep 27, 2015

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

Explanation:

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