Answered: There are four slices of pizza left to…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

There are four slices of pizza left to choose from. Each slice of pizza has one topping. Three of the slices have sausage as a topping and the fourth slice has pepperoni as a topping. Kiran randomly selects one slice then Mai randomly selects one slice. What is the probability that Mai selects a slice of pepperoni pizza under the condition that Kiran selects a slice of sausage pizza?

Expert Solution

Step 1

The sample space S would consist of the combination of 1 pepperoni pizza and 3 sausage pizza which is $4 \times 3 = 12$ .

S={PS,PS,PS,SS,SS,SP,SS,SS,SP,SS,SS,SP}

n(S)=12

Event A indicates the combination in which Mai selects a slice of pepperoni pizza.

A={SP,SP,SP}

n(A)=3

$P (A) = \frac{3}{12} = \frac{1}{4}$

Event B indicates the combination in which Kiran selects a slice of sausage pizza.

B={SS,SS,SP,SS,SS,SP,SS,SS,SP}

n(B)=9

P(B)= $\frac{9}{12} = \frac{3}{4}$

$A \cap B = {SP, SP, SP} n (A \cap B) = 3 P (A \cap B) = \frac{3}{12} = \frac{1}{4}$

We have to find the probability that Mai selects a slice of pepperoni pizza under the condition that Kiran selects a slice of sausage pizza i.e P(A|B)