Question

So I have a question and I am not sure what it means...

Compare P(A∩B) with P(A∪B), and explain what each probability means in the context of the situation and data you collected.

Answer 1

@ganeshie8 the table is the same:
Type krispy kreme dunkin donuts
home 5 2
bakery 7 6

Answer 2

easy, define \(A\) and \(B\) first

Answer 3

lets say
\(A\) : krispy kreme
\(B\) : home

Answer 4

\(P (A \cap B)\) means, "Probability of both A and B occurring"

Answer 5

look at the table,
how many like both "krispy kreme" and "home" ?

Answer 6

5

Answer 7

I am sorry @ganeshie8! I got busy with something else and took a lunch break. I am sorry! Thank you for replying and helping! When you get back on, can you continue to help me with this please?

Answer 8

@ganeshie8

Answer 9

So the answer for P(A∩B), it would be 5/12?

Answer 10

it should be 5/20

Answer 11

you need to divide by total number of students

Answer 12

and, P(A∪B) represents "probability for either A or B or both"

Answer 13

Oh okay so the answer for P(A∩B) is 1/4 when simplified. So then would P(A∪B) be 1/4 or 12/20 (or 3/5)? I get 12/20 because I added the home and the bakery under krispy kreme. Am I doing this correct?

Answer 14

12/20 simplifies to 3/5, that is where 3/5 came from

Answer 15

denominator is right

Answer 16

how did u get 12 for numerator ?

Answer 17

Okay :) I added 5 (home) + 7 (bakery) to get 12 total under the krispy kreme row.

Answer 18

I mean under the krispy kreme column

Answer 19

why did u leave "home AND dunken donuts" ?

Answer 20

u want either "home" or "kirspy kreme"

Answer 21

so A U B includes everyone in home, and everyone in kirspy kreme

Answer 22

So how do we solve it?

Answer 23

everyone in home : 5 + 2 = 7
everyone in krispy kreme : 5 + 7 = 12

add them : 19
however we have added 5 times, so subtract 5 : 19 - 5 = 14

Answer 24

so P(A U B) = 14/20

Answer 25

simplify

Answer 26

Oh okay. So simplified it would be 7/10?

Answer 27

correct !

Answer 28

okay! Thank you so much! I get it now! :)

Answer 29

Does this sound good?

A : krispy kreme
B : home
P(A∩B) means Probability of both A and B occurring
In the home column under Krispy Kreme, we have 5. This will be the numerator since we are finding the probability of people who eat Krispy Kreme at home as opposed to the probability of people eating Krispy Kreme at the Bakery, eating Dunkin Donuts at Home, and eating dunkin donuts at the bakery. So the denominator is going to be 20 since 5 + 7 = 12, 12 + 2 = 14, 14 + 16 = 20


P(A∪B) represents "probability for either A or B or both.
So what we do is find the sum of the home row. 5 + 2 = 7
Then we find the sum of the Krispy Kreme column. 5 + 7 = 12
Then we add the sums together. 7 + 12 = 19
Then, since we added 5 to both, we have to subtract 5. 19 - 5 = 14
Because the sum of all of the people total in the table is 20, we have to put 14 over 20. As you can see, we can simplify this to be 7/10.

Answer 30

looks good !!

Answer 31

good job :)

Answer 32

Thank you!!

Answer 33

u wlc !