2. Jeff is trying to "get with" Slater. Being a calculating player, Jeff knows that his population proportion of landing a date is 69 percent. Jeff is going to make advances on Slater until success, so let us model the situation with a geometric distribution.2 (a) What is the probability that Jeff needs exactly 3 advances? (b) What is the probability that Jeff needs at least 3 advances? (c) Given that Jeff already made 4 advances, what is the probability that Jeff will need at least 3 more advances? (d) Show that all of the possibilities do indeed add up to 100 percent.

Step-by-step explanation:

a) - The probability which Jeff requires at exactly three advances that is,

Then, put the value of in eq - i

b) - The probability which Jeff requires at least three advances that is,

Put the value of in the eq

c) - Considering that he has only made four advances, the probability would be that he will require at least three more advances that is.

Then, put the value in the eq - i

d) - Display that all possibilities actually added up to 100% that is.

by solving then, we get

So, we get 1 or 100%.

A) 0.0066309 ; B) 0.0961 ; D) Proven

Step-by-step explanation:

Geometric Distribution : X ~

p = 0.69 ; q = 1- p = 1 - 0.69 = 0.31

A) P (x = 3) =

B) P (x > 3) = 1 - [ P(x =1) + P(x = 2) ]

D) P (x > 1) = P (x =1) + P (x = 2) + P (x = 3) ...............

= p + pq + pq^2 + pq^3 ........ [Geometric series with a = p , r = q]

Sum of infinite geometric series = a / (1- r)

p / (1-q) = 0.69 / (1-0.31) = 0.69 / 0.69 = 1 {Hence Proven}