Question

Question about probability. I appreciate the help!

Answer 1

This table is an example of the principle of independence.
This table is not an example of the principle of independence.
There is not enough information to answer this question.

Answer 2

I need help understanding principle independence. @jim_thompson5910 Thanks!

Answer 3

How many people have a membership?

Answer 4

40

Answer 5

this is out of 70 people total

so P(has membership) = 40/70 = 4/7

Answer 6

what is the probability a person attends one or more of the classes offered?

Answer 7

31--that is if we are talking about people with and without memberships. Only with memberships is 17 and without membership is 14.

Answer 8

so the probability someone attends 1 or more classes is 31/70

Answer 9

now IF the two events (shown below)

* has membership
* attends 1 or more classes

are independent, then

P( has membership AND attends 1 or more classes) = P(has membership) * P(attends 1 or more classes)

Answer 10

does that look familiar?

Answer 11

Yes, it does. So, P(40) * P(31) =1240 Right?

Answer 12

And the answer would be: This table is an example of the principle of independence. (choices listed above)

Answer 13

P( has membership AND attends 1 or more classes) = P(has membership) * P(attends 1 or more classes)

P( has membership AND attends 1 or more classes) = (4/7) * (31/70)

P( has membership AND attends 1 or more classes) = 62/245

do you see how I got that?

Answer 14

oh! *slaps forehead* Yes, sorry I wasn't thinking and ignored what you'd said before about the problem. I understand it now.

Answer 15

how many people fit these requirements

has membership AND attends 1 or more classes

Answer 16

Isn't that just what we solved for? 62/245? And how does this correlate to the principle of independence?

Answer 17

look for the "has membership" row
and
the "1 or more classes" column

what number is there?

Answer 18

17

Answer 19

@jim_thompson5910 when you finish here can u please visit the link in ur notification this question needs a 2nd opinion thanks

Answer 20

since it's 17 out of 70 total

the actual probability P( has membership AND attends 1 or more classes) should be 17/70

Answer 21

and not 62/245

Answer 22

you only multiply IF the two events are independent

thinking in reverse, if you can multiply and get the same result as looking in the table, then the events are independent

Answer 23

but 17/70 is not equal to 62/245

so they are not independent events

Answer 24

Thank you so much! You explained everything very well. So, this table is not an example of the principle of independence because the two events don't equal each other?

Answer 25

correct, there is some connection between the two events (one event is dependent on the other somehow)

Answer 26

Okay, thank you so much. You are amazing!

Answer 27

you're welcome