Probability

[umaa]

A jar contains marbles of several different colors. Some marbles are to be taken from the jar one at a time, examined and the put back in the jar. What is the probability that exactly three of next five marbles taken from the jar will be blue?

(1) The probability that all of the next five marbles taken from the jar are blue is 243/3125

(2) The probability that none of the next five marbles taken from the jar are blue is 32/3125

[sjd00d]

should be D.

1. probably of next 5 marbles - 243/3125. probably p of getting blue in first try than p^5 = 243/3125, from this you can find value for p^3..Sufficient

2. probably of getting 5 marbles 1 - 32/3125, calculate from this as #1..Sufficient

[ontopofit]

yes IMO D.

1) tells there are 5 marbles in which 3 are blue;suff
2) tells the same thing that out of 5 2 are not blue;suff

[aroon7]

I think it is A

1) says: The probability that all of the next five marbles taken from the jar are blue is 243/3125

P(5blue) = 243/3125
p(blue)^5 = 243/3125

from this we can find out P(blue) and P(not blue)
ans will be P(blue)*P(blue)*P(blue)*P(not blue)*P(not blue)

Suff.

2) says 'The probability that none of the next five marbles taken from the jar are blue is 32/3125"
so this is 1-Prob(1 blue U 2 blue U 3 blue U 4 blue U 5blue) = 32/3125
we dont have any info about other marbles in the jar
so this is insuff.

[dendude]

2) says 'The probability that none of the next five marbles taken from the jar are blue is 32/3125"
so this is 1-Prob(1 blue U 2 blue U 3 blue U 4 blue U 5blue) = 32/3125
we dont have any info about other marbles in the jar
so this is insuff.

This does not seem right.
From 32/3125 you can get [P(not Blue)]^5, from which you can get P(Blue), since 1-P(Blue) = P(not Blue)

So the Ans should be D

[aroon7]

2) says 'The probability that none of the next five marbles taken from the jar are blue is 32/3125"
so this is 1-Prob(1 blue U 2 blue U 3 blue U 4 blue U 5blue) = 32/3125
we dont have any info about other marbles in the jar
so this is insuff.

This does not seem right.
From 32/3125 you can get [P(not Blue)]^5, from which you can get P(Blue), since 1-P(Blue) = P(not Blue)

So the Ans should be D

dendue,

Following are the possible combinations:

b - blue
x - other color

BXXXX (5 times)
BBXXX (5C2 times)
BBBXX (5C3 times)
BBBBX (5c4 times)
BBBBB (1 time)

XXXXX (1 time)

so 32/3125 is prob of XXXXX
1 - 32/3125 gives you prob of other 5 combinations not just prob of BBBBB

if X is only one color we can calculate P(blue) but it is not explicitly stated...
so insuff

[umaa]

The OA is D. But I'm not clear with the explanations you've given. It because I'm bad at probability. Can you please post a detailed explanation? Also, can you send me a link or a way to strengthen my probability area?

[ontopofit]

yes aroon....ur right.
thats why 1-none will not give the probability of 5B's.

instead it is

(1-NB)^5.
hence D.

[dendude]

dendue,

Following are the possible combinations:

b - blue
x - other color

BXXXX (5 times)
BBXXX (5C2 times)
BBBXX (5C3 times)
BBBBX (5c4 times)
BBBBB (1 time)

XXXXX (1 time)

so 32/3125 is prob of XXXXX
1 - 32/3125 gives you prob of other 5 combinations not just prob of BBBBB

if X is only one color we can calculate P(blue) but it is not explicitly stated...
so insuff

Aroon,
I dont think its necessary to worry about other colors.
According to me there are only two outcomes: Blue or Not Blue. We do not have to be concerned about how many other colors there are.

Stmt#2 gives,
P(NB)*P(NB)*P(NB)*P(NB)*P(NB) = 32/3125
i.e P(NB)^5 = 32/3125 from which you can derive P(NB) (which is 2/5)
P(B) can be easily derived from this and the value can be used to determine whats asked in the question.

So you can derive the required answer from either Stmts alone.
Hence D

[krisraam]

The Answer is D:

As we are replacing the balls after each try. The events are mutually exclusive.

Statement 1 says "The probability that all of the next five marbles taken from the jar are blue is 243/3125 "

Let the probabilty of taking a blue ball is x/y. If 5 you do that five times the probabilty is (x/y)^5 = 243/3125

So the probabilty of taking a blue ball is 3/5.

Probability of not taking a blue ball is 1-3/5 = 2/5.

Probabilty of taking a blue ball 3 times in 5 passes is (3/5)^3 * (2/5)^2

statement 1 is sufficient.

Statement 2 says "The probability that none of the next five marbles taken from the jar are blue is 32/3125"

Probabilty of not taking a blue ball in all of the 5 times is 32/3125.

Probability of not taking a blue ball is 2/5 ( this means 2 out of 5 times you will get a color other than blue)

Probabilty of taking a blue ball is 1-2/5 = 3/5

Statement 2 is also sufficient.

Statement 1 and 2 gives the same information.

Thanks
Raama