Question

Question #05ff8

Answer 1

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