anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
how many marbles total?
anonymous
  • anonymous
9
anonymous
  • anonymous
how many purple?

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More answers

anonymous
  • anonymous
7
anonymous
  • anonymous
what is the probability of selecting a purple one first?
anonymous
  • anonymous
7/9?
anonymous
  • anonymous
yes, good. now hold on to that number, we are going to need it again
anonymous
  • anonymous
now that you have selected a purple marble, how many marbles are left?
anonymous
  • anonymous
6 purple marbles left, and 8 total marbles left.
anonymous
  • anonymous
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
anonymous
  • anonymous
2 white marbles are left
anonymous
  • anonymous
good, so what is the probability that the next marble selected is white?
anonymous
  • anonymous
2/8?
anonymous
  • anonymous
exactly (better known as \(\frac{1}{4}\) )
anonymous
  • anonymous
to finish the problem, multiply the two probabilities i.e. compute \[\frac{7}{9}\times \frac{1}{4}\]
anonymous
  • anonymous
so that's 7/36?
anonymous
  • anonymous
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
anonymous
  • anonymous
procedure for the probability that both are white is the same, although the answer is of course different
anonymous
  • anonymous
let me know if you need help with that one too the idea is identical
anonymous
  • anonymous
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?
anonymous
  • anonymous
@satellite73
anonymous
  • anonymous
yes
anonymous
  • anonymous
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
anonymous
  • anonymous
no not tired of you
anonymous
  • anonymous
first off it is entirely obvious that it is more likely to get two purple than two white, because there are more purple
anonymous
  • anonymous
That is what i was thinking
anonymous
  • anonymous
I just wanted to make sure
anonymous
  • anonymous
but we know now how to compute both probabilities two white you just computed and got \(\frac{2}{9}\times \frac{1}{8}=\frac{1}{36}\)
anonymous
  • anonymous
Yep
anonymous
  • anonymous
two purple is \[\frac{7}{9}\times \frac{6}{8}=\frac{7}{12}\]
anonymous
  • anonymous
So, two white is: 2/9 x 1/8 = 1/36
anonymous
  • anonymous
right
anonymous
  • anonymous
Ok, I got it, thanks! @satellite73
anonymous
  • anonymous
yw

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