Question

A bag contains 2 white marbles and 7 purple marbles. Two marbles are drawn at random. One marble is drawn and not replaced. Then a second marble is drawn.
a. What is the probability of selecting a purple marble and then a white marble?
b. What is the probability of selecting two white marbles?
c. Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row? Show your work.

Answer 1

how many marbles total?

Answer 2

9

Answer 3

how many purple?

Answer 4

7

Answer 5

what is the probability of selecting a purple one first?

Answer 6

7/9?

Answer 7

yes, good.
now hold on to that number, we are going to need it again

Answer 8

now that you have selected a purple marble, how many marbles are left?

Answer 9

6 purple marbles left, and 8 total marbles left.

Answer 10

right
but we need to know how many WHITE marbles are left, because now we have to compute the probability that the next marble selected is white

Answer 11

2 white marbles are left

Answer 12

good, so what is the probability that the next marble selected is white?

Answer 13

2/8?

Answer 14

exactly (better known as \(\frac{1}{4}\) )

Answer 15

to finish the problem, multiply the two probabilities
i.e. compute
\[\frac{7}{9}\times \frac{1}{4}\]

Answer 16

so that's 7/36?

Answer 17

it is the probability that the first marble chosen is purple \(\frac{7}{9}\) times the probability that the second marble chosen in white GIVEN that the first one was purple \(\frac{1}{4}\)
yes , \(\frac{7}{36}\) is right

Answer 18

procedure for the probability that both are white is the same, although the answer is of course different

Answer 19

let me know if you need help with that one too
the idea is identical

Answer 20

I think I have the answer for this part: b. What is the probability of selecting two white marbles? Is it this: 2/9*1/8=1/36, right?

Answer 21

@satellite73

Answer 22

yes

Answer 23

Ok I have part c(the last part finally) Can you help please, then I promise I will leave you alone, you are probably getting tired of me: c. Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row? Show your work. @satellite73

Answer 24

no not tired of you

Answer 25

first off it is entirely obvious that it is more likely to get two purple than two white, because there are more purple

Answer 26

That is what i was thinking

Answer 27

I just wanted to make sure

Answer 28

but we know now how to compute both probabilities
two white you just computed and got \(\frac{2}{9}\times \frac{1}{8}=\frac{1}{36}\)

Answer 29

Yep

Answer 30

two purple is
\[\frac{7}{9}\times \frac{6}{8}=\frac{7}{12}\]

Answer 31

So, two white is: 2/9 x 1/8 = 1/36

Answer 32

right

Answer 33

Ok, I got it, thanks! @satellite73

Answer 34

yw