A bag has 1 red marble, 4 blue marbles, and 3 green marbles. Peter draws a marble randomly from the bag, replaces it, and then draws another marble randomly. What is the probability of drawing 2 blue marbles in a row?

Question

KingPizza · Answer

first do you know the probability of drawing just 1 blue marble in a row?

mykenzie · Answer

ye its 7

mykenzie · Answer

1/8

KingPizza · Answer

so there are 8 marbles total, but there are 4 blue marbles total so it can't be 1/8

KingPizza · Answer

what should it be?

mykenzie · Answer

4/8

KingPizza · Answer

yes that's not the final answer though so do you know how to use that information to find the probability of picking two blue marbles in a row

mykenzie · Answer

k thxs

KingPizza · Answer

what answer did you get?

mykenzie · Answer

1/7 bc if u take one and don't replace it that would be 7

mykenzie · Answer

3/7

KingPizza · Answer

he places the already chosen marble back though so the denominator is still 8

mykenzie · Answer

k then 4/8
right?

KingPizza · Answer

well since you chose a blue marble the time before it has to be based on you choosing it two times in a row which is not as likely for any of the colors so device 4/8 by 2 for the final answer

KingPizza · Answer

because the probability has to be half of what it was before

mykenzie · Answer

k

KingPizza · Answer

so what did you get as your answer?

mykenzie · Answer

2/8 or 3/8

KingPizza · Answer

4/8 is the same thing as 1/2 or 0.5 so divide that by 2 and get 0.25 which is 2/8, which equals 1/4, so if you need simplest form, then put in 1/4 as the answer

mykenzie · Answer

k thks

Florisalreadytaken · Answer

@kingpizza wrote:

4/8 is the same thing as 1/2 or 0.5 so divide that by 2 and get 0.25 which is 2/8, which equals 1/4, so if you need simplest form, then put in 1/4 as the answer

this doesnt make any sense -- why did you divide 0.5, but not just multiply the fractions? it really is confusing

KingPizza · Answer

because it has to be less likely to draw TWO marbles in a row so if we multiplied the fractions, we would've gotten a higher percentage than the first time

Florisalreadytaken · Answer

what? no.

the fact that he puts that bue marble BACK in the bag, makes these 2 independent events.

so we can say that 
$$  P(1^{st} ~~ blue ~~ marble)=\frac{4}{8} \Rightarrow P(1)=\frac{1}{2} $$
whilst
$$  P(2^{nd} ~~ blue ~~ marble)=\frac{4}{8} \Rightarrow P(1)=\frac{1}{2}     $$  
lets just multiply the two:
$$ P(1 ~ and ~2) = \frac{1}{2} \times \frac{1}{2} \Rightarrow P(1 ~ and ~2) = \frac{1}{4}$$
this way you dont do the pointless decimals.

KingPizza · Answer

well it gave us the same results so I guess we can do it either way

KingPizza · Answer

yeah we're pretty much saying almost the same thing so neither of us is wrong about this