Question

A group of people were given a personality test to determine if they were Type A or Type B. The results are shown in the table below:

Answer 1

Compare P(Female or Type B) with P(Female | Type B).
There is not enough information.

P(Female or Type B) > P(Female | Type B)

P(Female or Type B) = P(Female | Type B)

P(Female or Type B) < P(Female | Type B)

Answer 2

how in god's green earth did we go from trig to probability in one jump?

Answer 3

P(Female or Type B) lets compute it

Answer 4

okay.

Answer 5

how many are female ?

Answer 6

22

Answer 7

or in total?

Answer 8

in total
all females

Answer 9

because the "or" means "or" not "and" so we need to count
all females not just some

Answer 10

97

Answer 11

yes
now for the "or" part we also need males that are type B
how many of those?

Answer 12

103

Answer 13

yes but we have to be careful
we already counted the female type B and we don't want to count them twice
how many male type B?

Answer 14

48?

Answer 15

right
to "type B or Female total" total is \(48+97=145\)

Answer 16

that is one or the other or both
now a quick count shows that the total number of people in the whole thing is \(55+75+48+22=200\)

Answer 17

okay!

Answer 18

making
\[P(\text{Female or Type B}) =\frac{145}{200}\]

Answer 19

this one is easier
P(Female | Type B).

Answer 20

70

Answer 21

yes
of those 70, how many are female?

Answer 22

22

Answer 23

good
that makes
\[P(\text{female}|\text{type B})=\frac{22}{70}\]

Answer 24

yeah

Answer 25

so is it the last option?

Answer 26

now your last job it to compare those numbers
probably need decimals for each but it should be pretty clear that \[\frac{145}{200}>\frac{22}{70}\]

Answer 27

so it's P(Female or Type B) < P(Female | Type B)

Answer 28

no your inequality is backwards

Answer 29

P(Female or Type B) > P(Female | Type B)

Answer 30

P(Female or Type B) > P(Female | Type B)

Answer 31

thank you :) x

Answer 32

yeah i think so
check the numbers we computed

Answer 33

yw