Question

A two-way frequency table shows baldness in men over 45 and men under 45.

Under 45 Over 45 Total
Bald 24 16 40
Not Bald 36 24 60
60 40 100


Based on this data, are baldness and being over 45 independent events?

A) Yes, P(bald | over 45) = P(bald)

B) Yes, P(bald | over 45) = P(over 45)

C) No, P(bald | over 45) ≠ P(bald)

D) No, P(bald | over 45) ≠ P(over 45)

Answer 1

A and B are independent, if P(A | B) = P(A)

Answer 2

to knw whether "baldness" and "over 45" are independent or not, find P(bald) first

Answer 3

p(bald) = ?

Answer 4

I have no idea what p(bald) is, what does that mean?

Answer 5

@ganeshie8

Answer 6

p(bald) means, probability for being "bald"

Answer 7

look at the given data,
look at last column

Answer 8

we have surveyed a total of "100" people right ?

Answer 9

yeah and 40 are bald so is p(bald)=4?

Answer 10

out of which, 40 are "bald" and 60 are not

Answer 11

40* not 4

Answer 12

so, probability for being bald = 40/100 = 4/10 = 2/5

Answer 13

p(bald) = 2/5

Answer 14

fine ?

Answer 15

right

Answer 16

next u need to find the probability for "bald" for ppl over 45 years

Answer 17

Look at second column

Answer 18

40 ppl are over 45 right ?

Answer 19

out of which, 16 ppl are bald and 24 ppl are not

Answer 20

so probability of baldness, given that they're over 45 = 16/40 = 2/5

Answer 21

p(bald | over 45) = 2/5

Answer 22

so we got the same probability for both :-

p(bald) = p(bald | over 45) = 2/5

Answer 23

so, the two events : baldness and over 45 are independent

Answer 24

see if that makes some sense...

Answer 25

I think I understand. Is the answer A then? @ganeshie8

Answer 26

A is \(\large \color{red}{\checkmark}\)

Answer 27

Thanks so much! :)

Answer 28

THis was correct (just took the test)! :) Ty

Answer 29

You explained how to solve it really well XD