According to the most recent adult demographic census of ohio, 22% of residents are 18 to 29 years old, 45% are between 30 and 49 years old, and 33% are 50 and older. (age brackets a1, a2, and a3 respectively.) of ag4596. those who are in the al age bracket, 5% use e-harmony: of those in a2, 19% use e-harmony; and of those in , compute the joint probabilities where e an individual uses e-harmony (it will be to use a probability tree)
p(a1ne)
p(a2ne)
a) what proportion of residents use e-harmony?
b) you receive a message from an individual using e-harmony expressing interest. what is the probability the individual is 50 years or older?

a)

Since we have all the possible values we can replace:

And that would be the proportion of residents who use E-Harmony

We can find the P(A1nE)  and P(A2nE) with the following formulas:

b)  For this case we want this probability

And from the Bayes conditional probability we have this:

Step-by-step explanation:

Notation

represent the event resident between 18 and 29 years old

represent the event resident between 30 and 49 years old

represent the event resident is >50 yeard old

represent the event the residen tuse E-Harmony

From the problem we have the following probabilities:

And we have conditional probabilites also given:

The other probability assumed since the problem is incomplete is:

Part a

For this case we can use the total probability rule given by:

Since we have all the possible values we can replace:

And that would be the proportion of residents who use E-Harmony

We can find the P(A1nE)  and P(A2nE) with the following formulas:

Part b

For this case we want this probability

And from the Bayes conditional probability we have this:

the diameter is 16 cm. are you a teacher?

step-by-step explanation: