Question

The marketing research department at the Fresno Mall plans to survey teenagers about a newly developed soft drink. 70% of the people surveyed said they like the orange flavored soda. 35% of the people surveyed said they liked the orange flavored soda AND the lime flavored soda. Using this information and the Text Editor, answer the following questions:

1.What is conditional probability?

2.Explain the formula for conditional probability.

3.Explain how to solve this example.

What percent of those who liked orange flavored soda also like lime flavored soda, and how did you come to that conclusion?

Answer 1

Hello.

1. conditional probability is a measure of the probability of an event.If A and B are two events such that given event B has happened and we have to find the probability of event A, then probability of A given B, denoted by P(A/B) is given by.

2. P(A/B) = P(A∩B)/P(B)

3. You would put it like

Give that P(A) = 70, P(B) = 35 and P(A∩B) = 70/35


4. The pengatge is 35% because you need a % out off 100.


Have a nice day

Answer 2

50% of those who liked orange flavored soda also like lime flavored soda.

Explanation:

Let A and B represents the following events.

A : The people like the orange flavored soda.

B : The people like the lime flavored soda.

It is given that 70% of the people surveyed said they like the orange flavored soda.

`P(A)=70\%=0.70`

35% of the people surveyed said they liked the orange flavored soda AND the lime flavored soda.

`P(A\cap B)=35\%=0.35`

(1)

Conditional probability : It is the probability of an event or outcome occurring, based on the occurrence of a previous event or outcome.

(2)

If we have two events X and Y, and we need to find the probability of event X as event Y is given then the formula for conditional probability is

`P((X)/(Y))=(P(X\cap Y))/(P(Y))`

(3)

We need to find the percent of those who liked orange flavored soda also like lime flavored soda.

`P((B)/(A))=(P(A\cap B))/(P(A))`

Substitute P(A)=0.70 and P(A∩B)=0.35 in the above formula.

`P((B)/(A))=(0.35)/(0.70)`

`P((B)/(A))=0.5=50\%`

Therefore, 50% of those who liked orange flavored soda also like lime flavored soda.