Question

A mutual fund salesperson has arranged to call on four people tomorrow. Based on past experience the salesperson knows that there is a 20% chance of closing a sale on each call. Determine the probability distribution of the number of sales the salesperson will make.

Let S denote success, i.e. closing a sale P(S) =0.20 Thus Sc is not a closing sale, and P(Sc)=.80

Answer 1

Sample space S = 0 , 1 , 2 , 3 , 4

S ~ Binomial (n,p)

Where n = 4 , p = 0.20

P(S) = ⁿCs 0.20^s 0.80^n-s

P(S = 0) = 0.80⁴

= 0.4096

P( S = 1) = ⁴C₁ 0.20¹ 0.80³

= 0.4096

P( S = 2) =  ⁴C₂ 0.20² 0.80²

= 0.1536

P( S = 3) =  ⁴C₃ 0.20³ 0.80¹

= 0.0256

P( S = 4) =  0.20⁴

= 0.0016

Probability distribution for S is

S	0	1	2	3	4
P(S)	0.4096	0.4096	0.1536	0.0256	0.0016