Liz has 2 red, 2 white, and 3 blue marbles in a cup. She draws two marbles at random and does not replace the first one. What is the probability that she will draw a white marble and then a blue marble or a blue then a red?

Question

Liz has 2 red, 2 white, and 3 blue marbles in a cup.  She draws two marbles at random and does not   replace the first one.  What is the probability that she will draw a white marble and then a blue marble or a blue then a red?

sasogeek · Answer

ok so umm there are a total of 7 marbles.
2 red
2 white
3 blue

the probability that she draws a white marble is 2/7 , if she picks a white marble but doesn't replace it, the total number of marbles left are 6. so the probability that she would then pick a blue marble will be 3/6. now she's not picking white OR blue, she's picking white AND blue... so our equation will be

$\large P(W_{1}nB_{2}) =\frac{2}{7}\times \frac{3}{6} = \frac{2}{14} $

anonymous · Answer

the key is 2/7

sasogeek · Answer

well i think i didn't answer the whole question lol, i forgot the last part

anonymous · Answer

I think you not finish

sasogeek · Answer

if she picks a blue, then a red, the probability will be

$\large P(B_{1}nR_{2})=\frac{3}{7}\times \frac{2}{6}=\frac{1}{7} $

not that she's picking white then blue OR blue then red
this means that we have to ADD the 2 probabilities
so that would be
$\large \frac{1}{7}+\frac{1}{7}=\frac{2}{7} $


note that $\large \frac{2}{14}=\frac{1}{7} $

anonymous · Answer

ok,ty

sasogeek · Answer

you're welcome :) glad i could help :)

sasogeek · Answer

btw i meant to say that "NOTE that she's picking white then ..." and not "NOT that she's picking white then ..." :)