- BeccaB003

Question about probability. I appreciate the help!

- katieb

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- BeccaB003

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.

##### 1 Attachment

- BeccaB003

I need help understanding principle independence. @jim_thompson5910 Thanks!

- jim_thompson5910

How many people have a membership?

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## More answers

- BeccaB003

40

- jim_thompson5910

this is out of 70 people total
so P(has membership) = 40/70 = 4/7

- jim_thompson5910

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

- BeccaB003

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

- jim_thompson5910

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

- jim_thompson5910

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)

- jim_thompson5910

does that look familiar?

- BeccaB003

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

- BeccaB003

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

- jim_thompson5910

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?

- BeccaB003

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

- jim_thompson5910

how many people fit these requirements
has membership AND attends 1 or more classes

- BeccaB003

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

- jim_thompson5910

look for the "has membership" row
and
the "1 or more classes" column
what number is there?

- BeccaB003

17

- LynFran

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

- jim_thompson5910

since it's 17 out of 70 total
the actual probability P( has membership AND attends 1 or more classes) should be 17/70

- jim_thompson5910

and not 62/245

- jim_thompson5910

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

- jim_thompson5910

but 17/70 is not equal to 62/245
so they are not independent events

- BeccaB003

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?

- jim_thompson5910

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

- BeccaB003

Okay, thank you so much. You are amazing!

- jim_thompson5910

you're welcome

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