Question

Are A and B dependent or independent events?

Answer 1

The probabilities for each event are given by the ratio of the area of the even to the total area of 72. For example, Event C is Red Only.

Answer 2

Event A looks like it's composed of the blue and green regions. What is the area of the blue region? How about the green region?

Answer 3

All of the colors have equal area (18).

Answer 4

this means that the area of the blue and green regions is 36, agreed?

Answer 5

Yes.

Answer 6

If you took a dart and randomly threw it at the board, what is the probability you land in region A? In other words, what is the probability you land in the green or blue regions?


Hint: you'll be dividing 2 values

Answer 7

A 50% chance, right? 36/72 = 1/2

Answer 8

good, how about for region B?

Answer 9

It would also be 50%

Answer 10

yep

Answer 11

so far you've shown that

P(A) = 0.5
P(B) = 0.5

Answer 12

now let's move onto the green region only. This is the region where both A and B overlap. This is the event where BOTH events happen at the same time

If you throw a dart randomly, what are the chances it lands in the green region?

Answer 13

25%

Answer 14

good

Answer 15

so far we know this information
P(A) = 0.5
P(B) = 0.5
P(A and B) = 0.25

Answer 16

Now we use this rule

If A and B are independent events, then the following equation holds true

P(A and B) = P(A)*P(B)

Answer 17

if you can show that `P(A and B) = P(A)*P(B)` is true, then you've shown that A and B are independent events

Answer 18

0.25 does equal 0.5 times 0.5, so they're independent!

Answer 19

yep you are correct

Answer 20

Thank you very much for your help

Answer 21

no problem