Question

Given that events A and B are independent, what is P (A|B)?

Answer 1

As per the definition of independent events...
P(A|B) = P(A)

(In other words, the event B has no effect on event A)

Another useful definition would be
A and B are independent if
\[\large P(A\cap B) = P(A)P(B)\]

Answer 2

thank you, help me with one more question?

Answer 3

Sure.

Answer 4

this one is a little longer.

In a survey of students at a local high school, 30% of the students said they liked tater tots and 15% of the students said they like French fries. If every one of the students who said they like French fries also said they like tater tots, what proportion of the students responding to the survey said they liked at least one of the two side dishes?

Answer 5

Tricky, you have to find the percentage of students who like at least one of these side dishes...
thankfully, those who like French Fries also like Tater Tots, so you can just count the students who like tater tots :)

Answer 6

okay!

Answer 7

wait, i don't understand

Answer 8

Okay, so we're counting the number of students who like tater tots or who like french fries, aye?

Answer 9

yes

Answer 10

So, what percent of these students like tater tots?

Answer 11

30%

Answer 12

and 15% like french fries...
however, those 15% also like tater tots, yes?

Answer 13

yeah

Answer 14

So they've already been counted among the 30% who like tater tots.

Answer 15

oh okay!

Answer 16

Okay, here's another way to look at it...

Answer 17

We want to count the number of students who like either tater tots or french fries.
This thingy represents them that like tater tots.

Answer 18

And the students that like french fries, well, they also like tater tots, so the students who like french fries go here...