Question

urn 1 contains 3 red balls and 4 black balls. urn 2 contains 4 red balls and 3 black balls. urn 3 contains 2 red balls and 6 black balls. if an urn is selected at random and a ball is drawn, find the probability it will be red

Answer 1

Okay, so assuming we pick urn 1, what is the probability we get a red ball from it?
And for urn 2?
and urn 3?
etc.


Let's just start here.

Answer 2

@carlo26 Can you do this?

Answer 3

Remember that: \[
\Pr(A|B) = \frac{\Pr(A \cap B)}{\Pr(B)}
\]

Answer 4

1. 3/7 2. 4/7 3. 2/8

Answer 5

Now, what is the probability that you urn 1 is selected?

Answer 6

1/3 ?

Answer 7

Right.

Answer 8

By the way, what class are you taking? Do you understand what that formula I gave up there meant?

Answer 9

intro to prob & stats.. no, i didn't lol

Answer 10

so the answer is 1/3? lol

Answer 11

No.

Answer 12

ok.. what do i do now, after i got that?

Answer 13

Basically, you calculated the probability of picking a red ball from urn 1 IF you knew that a ball was picked from urn 1.

If you multiply these probabilities, you will get the probability that you picked urn 1 and picked a red ball from it.

Answer 14

So the probability of picking urn 1 AND picking a red ball is: \(\frac{3}{7} \times \frac{1}{3}\).

Answer 15

Now you need the probability picking urn 2 AND picking a red ball...

and the same for picking urn 3 AND picking a red ball

Answer 16

Once you have calculated all three, the probability of picking a ball from any of them is adding those 3 together.

Answer 17

i hate this stuff lol.. thanks for the great helping though!

Answer 18

prob of urn 2 and picking a red ball is 1/3 and 4/7, right?

Answer 19

multiplied

Answer 20

yea.. so i just multiply all 3 of the things after i multiply them individually?

Answer 21

no you add them up

Answer 22

k

Answer 23

thus reqd prob =1/3(3/7 +4/7 +2/8)=5/12