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.

Male Female
Type A 55 75
Type B 48 22

Answer 1

@kropot72

Answer 2

Compare P(Female or Type B) with P(Female | Type B). (5 points)


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 3

Not sure what the question is asking : /

Answer 4

To solve this you first need to sum the row and the column totals.

Answer 5

Okay so Type A total is 130, Type B total is 70. Female is 97, Male is 103.

Answer 6

P(F) = 97/200
P(M) = 103/200
P(A) = 130/200
P(B) = 70/200
\[\large P(F \cup B)=P(F)+P(B)-P(F \cap B)=you\ can\ calculate\]

Answer 7

And this will tell me the answer?

Answer 8

Compare the result with:
\[\large P(F|B)=\frac{22}{70}\]

Answer 9

i'm really confused @kropot72

Answer 10

@kropot72 how do i find P(F upside down U thing B)?

Answer 11

\[\large P(F \cap B)=P(F) \times P(B)\]

Answer 12

ahh okay, let me try and figure it out

Answer 13

so 167/200 - 6790?

Answer 14

No. Where did you get 6790 from?

Answer 15

P(f) x P(b)

Answer 16

\[\large P(F) \times P(B)=\frac{97}{200}\times\frac{70}{200}=\frac{97\times70}{200\times200}=?\]

Answer 17

OH okay hold on

Answer 18

so it'd be 167 / 200 - 0.16975?

Answer 19

@kropot72

Answer 20

Correct.

Answer 21

Okay, and so how does this exactly relate to the answer? @kropot72

Answer 22

@kropot72 !

Answer 23

You need to compare the results of:
P(female or type B) which is written in correct symbols as:
\[\large P(F \cup B)\]
and P(female | given type B) which is written in correct symbols as:
\[\large P(F|B)\]
So you need to finish the two calculations, and then choose the correct answer.

Answer 24

what exactly does P(F|B) mean? and is the answer D?

Answer 25

@

Answer 26

@kropot72

Answer 27

As I told you in my previous post:
P(female | given type B) is written in correct symbols as:
\[\large P(F|B)\]
Why don't you know these symbols if you are studying stats at this level?

Answer 28

It's a remedial course and I had to leave for a week to volunteer, so I'm back now and this specific type of question was always hard for me. :(

Answer 29

I don't understand what the | is though. @kropot72

Answer 30

It is a symbol for writing the conditional probability that B occurs if A has occurred in the following way:
P(B|A)
It can be read as 'the probability of B given A'.

Answer 31

okay wait! i think i have it. @kropot72 it's C right?

Answer 32

because p(f|b) is 48, and the other choice is more than 48. does that sounds right?

Answer 33

The maximum possible value of probability is 1.0000.
I already posted that:
\[\large P(F|B)=\frac{22}{70}=you\ can\ calculate\]

Answer 34

ok and so this is where i'm not too sure where to go?

Answer 35

the other is P(F or B), so wouldn't that clearly be bigger? @kropot72

Answer 36

i'm sorry if this is frusturating for you.

Answer 37

\[\large (F \cup B)=0.835-0.17=0.665\]
\[\large P(F|B)=0.314\]
\[\large P(F \cup B) >P(F|B)\]
Please post the exact wording of your choice of answer.

Answer 38

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 39

Okay, so I think I was right? The answer is B??

Answer 40

Yes, the second choice of answer is correct.
"P(Female or Type B) > P(Female | Type B"

Answer 41

Thank you so much!!! :)

Answer 42

You're welcome :)