Lesson: Determining Independence

Comment on Determining Independence

Can we answer the last question explained in this video as (4C2)÷(7C2)?
Thank U
greenlight-admin's picture

That's a perfect solution! It uses counting techniques.

Alternatively, we can use probability rules to say:

P(2 women selected) = P(1st selection is a woman AND 2nd selection is a woman)

= P(1st selection is a woman) x (2nd selection is a woman)

= 4/7 x 3/6

= 2/7

Hi brent,
I found a question from extra practice in khans academy, below is the question.
"There are 150 students in an eleventh grade high school class. There are 45 students in the soccer team and 35 students in the basketball team. Out of these students, there are 20 who play on both teams.
Let A be the event that a randomly selected student in the class plays soccer and B be the event that the student plays basketball. Based on this information, answer the following questions"

They came to the following conclusion after calculating { P(A) (is not equal to) P(B|A) } hence they are dependent event.

My question is, is this true can i come to conclusion
-----{ P(A) (is not equal to) P(B|A) } hence they are dependent event.
------{ P(A) = P(B|A) } hence they are independent event.

Why are these valid statement. Thank you in advance
greenlight-admin's picture

Are you sure you transcribed the information correctly?

If P(A) = P(A|B), then we can say that the events are independent.
Notice that event B occurring has no effect on event A occurring.
This is why they are independent.

Conversely, P(A) ≠ P(A|B), then we can say that the events are dependent.

Does that help?

Cheers,
Brent

Yes, thank you sir.

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