1 At Beth & Mary\'s Ice Cream Emporium customers always choose one topping to sp

Question

1 At Beth & Mary's Ice Cream Emporium customers always choose one topping to sprinkle on their ice cream. The toppings are classified as either candy (C) or fruit (F) toppings. Consider the chance experiment where the choice of toppings -- (C) or (F) -- is recorded for each of the next two customers who order ice cream. What is the probability the next 2 customers order fruit (F) ?

2Consider Beth & Mary's Ice Cream Emporium counted the selections of C or F for Friday and found C was chosen by 20 customers and F by 10. What is the probability that the next 2 customers order fruit (F) ?

Problem 2 (5 pts) (the symbol is the vertical line)

RxA RxB

srvive : 89 201

non survive : 52 101

1. Calculate the probability P(S Rx A):
2. Calculate the probability P(S Rx B):
3. Calculate probability P( Rx A NS)
4. Calculate probability P ( Rx B NS)
5. Which treatment was better.

Explanation / Answer

Problem1

Question1

As the probability of the choice of choosing a candy of a fruit is not given

Lets assume that the probability of choosing a candy is p

Hence the probability of choosing a fruit is 1-p

Hence next two customers order a fruit=joint prob of both the customers=(1-p)*(1-p)=(1-p)^2

Similary for the next two to order candy=p^2

and among the two,one to order a candy and other a fruit=2*p(1-p)

Given the value of p,one can calculate the value of the probability

Question 2

Here we are given the value of p=20/30=2/3

Hence the next 2 customers will order a fruit=(1/3)^2=1/9=0.11

Problem 2

1)P(S|RxA) =89/(89+52)=0.6312

2)P(S|RxB)=201/(201+101)=0.6655

3)P(RxA|NS)=52/(52+101)=0.34

4)P(RxB|NS)=101/(52+101)=0.66

5)In treatment RxB,both the chance of survival and non survival is more.But the difference between RxA and RxB for survival is marginally greater than RxA whereas the difference for non survival is large.

Hence for the sake of survival,I would believe treatment RxA is better.

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