# Thread: I seriously need help with these...

1. ## I seriously need help with these...

There are 6 true/false questions:

P(5 true)
p(exactly 3 true)

There are 5 blue marbles, 2 yellow marbles, and 6 green marbles.

P(pick 2 blue marbles, with replacement)
P(pick 2 blue marbles, without replacement)
P(pick 2 yellow marbles or 2 green marbles, without replacement)

There are 5 blue marbles, 2 yellow marbles, and 6 green marbles.

P(pick 2 blue marbles, with replacement)
P(pick 2 blue marbles, without replacement)
P(pick 2 yellow marbles or 2 green marbles, without replacement)
P(pick 2 marbles, with replacement)=P(blue marble)*P(blue marble)=
P(blue marble)^2. P(blue marble)= (number of blue marbles)/(total number of marbles). So, P(blue marble)=5/13

P(blue marble)^2=(5/13)^2=25/169. P(pick 2 blue marbles, with replacement)=25/169

P(pick 2 blue marbles, without replacement)=P(pick one of five desried marbles from total thirteen marbles)*P(pick one of four remaining desired marbles from total twelve remaining marbles)=
5/13*4/12=5/39

Last one's a bit trickier, but only a bit.
P(pick 2 yellow marbles or 2 green marbles, without replacement)=P(pick two yellow marbles, without replacement)+P(pick two green marbles, without replacement). Now, follow the steps from the second problem (but of course, use the number of yellow and green marbles, instead of the number of blue ones). So,

P(pick 2 yellow marbles, without replacement)=P(pick one of two desried yellow marbles from total thirteen marbles)*P(pick the remaining desired yellow marble from total twelve remaining marbles)=
2/13*1/12=1/78

P(pick 2 green marbles, without replacement)=P(pick one of six desried green marbles from total thirteen marbles)*P(pick one of five remaining desired green marbles from total twelve remaining marbles)=
6/13*5/12=5/26.

Now, add the two together. 1/78+5/26=1/78+15/78=16/78=8/39.

To review,
P(pick 2 blue marbles, with replacement)=25/169
P(pick 2 blue marbles, without replacement)=5/39
P(pick 2 yellow marbles or 2 green marbles, without replacement)=8/39

There are 6 true/false questions:

P(5 true)
be specific. when you say 5 true, do you mean EXACTLY 5 true?

p(exactly 3 true)
the solution here is similar to the solution for the last. we use the binomial distribution (look it up).

the probability is given by: $\displaystyle P(3) = {6 \choose 3}(1/2)^3(1/2)^3$

(why is that?)

any questions?