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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.
How many people have a membership?
this is out of 70 people total so P(has membership) = 40/70 = 4/7
what is the probability a person attends one or more of the classes offered?
31--that is if we are talking about people with and without memberships. Only with memberships is 17 and without membership is 14.
so the probability someone attends 1 or more classes is 31/70
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)
does that look familiar?
Yes, it does. So, P(40) * P(31) =1240 Right?
And the answer would be: This table is an example of the principle of independence. (choices listed above)
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?
oh! *slaps forehead* Yes, sorry I wasn't thinking and ignored what you'd said before about the problem. I understand it now.
how many people fit these requirements has membership AND attends 1 or more classes
Isn't that just what we solved for? 62/245? And how does this correlate to the principle of independence?
look for the "has membership" row and the "1 or more classes" column what number is there?
since it's 17 out of 70 total the actual probability P( has membership AND attends 1 or more classes) should be 17/70
and not 62/245
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
but 17/70 is not equal to 62/245 so they are not independent events
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?
correct, there is some connection between the two events (one event is dependent on the other somehow)
Okay, thank you so much. You are amazing!