Mathematics, 21.04.2020 23:38 isabelgalvarado2838

Suppose 20% of the population are 65 or over, 26% of those 65 or over have loans, and 53% of those under 65 have loans. Find the probabilities that a person fits into the following categories. (a) 65 or over and has a loan (b) Has a loan (c) Are the events that a person is 65 or over and that the person has a loan independent? Explain.

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Answer from: hey524

The probability that a person is 65 or over and has a loan is 0.052, the probability that a person has a loan is 0.476, and the probability that a person is 65 or over and that the person has a loan independent is 0.0952.

Given :

Suppose 20% of the population are 65 or over, 26% of those 65 or over have loans, and 53% of those under 65 have loans.

Let A represent the person who is 65 or more and B represents the person who has a loan.

If (P(A) = 20% = 0.2) then (P(A') = 1 - 0.2 = 0.8)

If (P(B|A) = 26% = 0.26) then (P(B'|A) = 1 - 0.26 = 0.74)

If (P(B|A') = 53% = 0.53) then (P(B'|A') = 1 - 0.53 = 0.47)

a) The probability that a person is 65 or over and has a loan is:

$\rm = P(A\cap B)$

$\rm = P(B|A)\times P(A)$

$=0.26\times 0.2$

= 0.052

b) The probability that a person has a loan is:

$\rm P(B) = P(A\cap B)+P(B\cap A')$

$\rm = P(B \cap A)+P(A')\times P(B|A')$

$=0.52+0.8\times 0.53$

= 0.476

c) The probability that a person is 65 or over and that the person has a loan independent is:

$= \rm P(A\cap B)$

= P(A).P(B)

= (0.2) $\times$ (0.476)

= 0.0952

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Answer from: jkirby29

(a)The probability that a person 65 or over and has a loan is 0.052.

(b)The probability that a person 65 or over and has a loan is 0.476

Step-by-step explanation:

Conditional probability:

Let A and B any two event is connected to a given random experiment E. The conditional probability of the event A on the hypothesis that the event B is occurred, denoted by P(A|B), is defined as,

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

So, P(A∩B) = P(B).P(A|B)

Given that,

The age of 20% of population are 65 years or over.

26% of those whose age 65 years or more have loans.

53% of those whose age under 65 years have loans.

E= the person is 65 or more.

F= the person has loan.

P(E)= 20%=0.2

P(F|E)=26%=0.26

P(F|E')=53%=0.53

So,

P(E')=1-0.2=0.8

P(F'|E)= 1-0.26=0.74

P(F'|E')= 1-0.53=0.47

(a)

The probability that a person 65 or over and has a loan is

=P(E∩F)

=P(F|E).P(E)

=0.26×0.2

=0.052

(b)

A person who has a loan either 65 or more , or under 65.

P(F)= P(F∩E)+P(F∩E')

=P(F∩E)+P(E').P(F|E')

= 0.052+ (0.8).(0.53)

=0.476

(c)

Independent event:

If A and B are two independent event,

Then,P(A∩B)=P(A).P(B)

The probability that a person is 65 or over and has a loan independent is

=P(E∩F)

=P(E).P(F)

=(0.2)×(0.476)

=0.0952

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water molecules will move from the side of higher water concentration to the side of lower concentration until both solutions are isotonic. at this point, equilibrium is reached. in an isotonic solution, the flow of water in and out of the cell is happening at the same rate.

hope this < 3

Answer from: Quest

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Suppose 20% of the population are 65 or over, 26% of those 65 or over have loans, and 53% of those u...