Question

17.3% of Sweden's population are at least 65 years of age, 49.5% are younger than 40 and
58.8% are between 20 and 65. Consider the experiment that randomly chooses an inhabitant of
Swedent.
i) What is the probability that this person is between 20 and 40 years old?

Answer 1

\[
\Pr(A\cup B) = \Pr(A)+\Pr(B)-\Pr(A\cap B)
\]Gives us: \[
\Pr(A\cap B) = \Pr(A)+\Pr(B)-\Pr(A\cup B)
\]

Answer 2

what i did was use the P(A and B) formula

so 58.8% x 49.5% = 29.1%

would that be wrong?

Answer 3

\(A\) will be the event that you are younger than 40, \(B\) will be the event you are older than 20.

Answer 4

We know that \(\Pr(A) = 0.495\)

Answer 5

@Sophie49 That formula only works for independent events. These are not independent events.

Answer 6

Being under 40 affects the likelihood you are between 20 and 65.

Answer 7

so the answer would be 31.5%

Answer 8

?

Answer 9

We need to find the probability that someone is over 20, okay?

Answer 10

okay how do we do that?

Answer 11

\(C\) is the even you are 20 - 65, \(D\) is the event you are 65+. \(B = C\cup D\) and there are mutually exclusive events. That means \[
\Pr(B) = \Pr(C)+\Pr(D) = 0.588+0.173
\]

Answer 12

Actually, come to think of it... I think we can utilize: \[
\Pr(A\cap B) = \Pr(\overline{\overline{A}\cup \overline{B}})
\]

Answer 13

Since \(\overline{A}\) and \(\overline{B}\) are mutually exclusive events... You cant be under 20 and over 40.

Answer 14

\[
\Pr(A\cap B) = \Pr(\overline{\overline{A}\cup \overline{B}}) = 1- \Pr(\overline{A}\cup \overline{B}) = 1-[(1-\Pr(A)) + (1-\Pr(B))]
\]

Answer 15

Okay so this is my strategy...\[\begin{split}
\Pr(A\cap B)
&= \Pr(\overline{\overline{A}\cup \overline{B}}) \\
&= 1- \Pr(\overline{A}\cup \overline{B}) \\
&= 1- [\Pr(\overline{A})+\Pr(\overline{B})] \\
&= 1-[(1-\Pr(A)) + (1-\Pr(B))]\\
&= 1-[(1-(0.495)) + (1-(0.588+0.173))]\\
\end{split}\]

Answer 16

That gives me 25.6%

Answer 17

why do you subtract the whole thing by 1?

Answer 18

\[
\Pr(\overline{A}) = 1-\Pr(A)
\]

Answer 19

\(A\) is some event, \(\overline{A}\) is the event that \(A\) doesn't happen.

Answer 20

We know \[
\Pr(A)+\Pr(\overline{A}) = 1
\]Because either an event happens, or it doesn't happen.

Answer 21

okay and then why did you add 0.588+0.173?

Answer 22

17.3% of Sweden's population are at least 65 years of age
58.8% are between 20 and 65

This means the probability that you are older than 20 is the sum of the two.

Answer 23

okay thanks!!!