ok so,
a bag contains 2 white marbles and 7 purple marbles. Two marbles are drawn at random one marbles drawn and replaced. then the second is drawn
1. what is the probability of selecting a purple marble and then a white marble?
2. what is the probability of selecting two white marbles?
3. is there a greater chance of selecting two white marbles in row or two purple marbles in row?

- anonymous

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- anonymous

i really need help please i dont understand

- Vocaloid

let's break the problem down step by step:
1. how many purple marbles are there?
2. how many total marbles are there?

- anonymous

7

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## More answers

- Vocaloid

yes, there are 7 purple marbles.
how many total marbles are there?

- anonymous

9

- Vocaloid

Excellent! so what is the probability of getting a purple marble?

- anonymous

7/9?

- Vocaloid

yes!
since the problem says "with replacement" that means that after we put the purple marble back, there are still 7 purple marbles and 2 white marbles.
my next question: what is the probability of getting a white marble?

- anonymous

2/9

- Vocaloid

great, you're doing very well so far!
ok, so #1 is asking "what is the probability of getting a purple marble AND a white marble"
that means you have to multiply the probability of getting a purple marble, times the probability of getting a white marble

- Vocaloid

in other words, the probability of getting purple, then white is: (probability of getting purple)*(probability of getting white)

- anonymous

so 7/9 X 2/9?

- Vocaloid

yup!

- anonymous

ok one sec

- anonymous

0.17283950617

- Vocaloid

uh, you don't have to do that, you can just leave it as a fraction
(7/9)*(2/9) = 14/81, do you agree?

- anonymous

oh ok yes

- Vocaloid

ok, do you think you can answer #2?
2. what is the probability of selecting two white marbles?

- anonymous

ummmmm 7/81?

- anonymous

14/81 right

- Vocaloid

hint: probability of getting a white marble: 2/9

- Vocaloid

no, the answer to number 1 is 14/81, let's find the answer to number 2 using the same logic
probability of getting two white marbles = (probability of getting one white marble)*(probability of getting one white marble)

- anonymous

ok

- anonymous

that would be 1/9 right?

- anonymous

si 1/9 x 1/9

- Vocaloid

not quite, please remember step 1:
what is the probability of getting a white marble?
there are 2 white marbles and 9 total marbles, remember?

- anonymous

yes

- Vocaloid

the probability of getting one white marble is 2/9, do you agree?

- anonymous

yes

- anonymous

so 2/9 x 2/9???

- Vocaloid

YES! excellent! you just finished #2, let's work on #3
what is the probability of getting two purple marbles?

- anonymous

so two is 4/81 right

- anonymous

?????

- Vocaloid

yes, number 2 is 4/81

- Vocaloid

let's work on number 3:
what is the probability of getting two purple marbles?

- anonymous

7/9 x 7/9?

- Vocaloid

great! now, what is the probability of getting two white marbles?

- anonymous

49/81 and 4/81?

- Vocaloid

great! now, which number is bigger?

- anonymous

49/81

- Vocaloid

great, so, can you answer question #3 now?

- Vocaloid

is there a greater chance of selecting two white marbles in row or two purple marbles in row?
purple or white, which one is bigger?

- anonymous

yes there is a greater chance a of getting 2 purple marble than 2 white marbles

- Vocaloid

AWESOME! you're done ~

- anonymous

THANK YOU SO MUCH

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