A bowl contains one marble labeled 0, one marble labeled 1, one marble labeled 2, one marble labeled 3. the bowl contains no other objects. If two marbles are drawn randomly without replacement, what is the probility that they willa dd up to 3 ?
(A)1/12
(B)1/8
(C)1/6
(D)1/4
(E)1/3
-thanx
probability
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A housing subdividion contains only 2 types of homes : ranch-style homes and townhomes. There are twice as many townhomes as ranch-homes. There are 3 times as many townhomes with pools than without pools. What is the probability that a home selected at random from the subdivision will be a townhome with a pool ?
(A)1/6
(B)1/5
(C)1/4
(D)1/3
(E)1/2
-thanx
(A)1/6
(B)1/5
(C)1/4
(D)1/3
(E)1/2
-thanx
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ttv,
In response to ur first Qs, I would like to take the following approach -
We can get 3 if we chose the following marbles -
(3,0) and (1,2) -> So number of chances = 2
But w/o any condition, we can take 2 marbles out of 4 in 4C2 = 6 ways [Here C -> Combination]
So probability = 2/6 = 1/3
Now according to ur second Qs,
Let, ranch-style homes = R and townhomes = T
and townhomes with pools = WT
and townhomes without pools = WoT
According to the problem, WT = 3WoT and T = 2R
So we can say WP + 3WoT = T
And WT + WoT = 2R
or 4WoT = 2R
or R = 2WoT
Total no of houses = T + R = 4WoT + 2WoT = 6WoT
And we have to select a WT from 6WoT.
So the probability = 3WoT/6WoT = 1/2 - So IMO E.
But what are the OAs? Please specify ...
In response to ur first Qs, I would like to take the following approach -
We can get 3 if we chose the following marbles -
(3,0) and (1,2) -> So number of chances = 2
But w/o any condition, we can take 2 marbles out of 4 in 4C2 = 6 ways [Here C -> Combination]
So probability = 2/6 = 1/3
Now according to ur second Qs,
Let, ranch-style homes = R and townhomes = T
and townhomes with pools = WT
and townhomes without pools = WoT
According to the problem, WT = 3WoT and T = 2R
So we can say WP + 3WoT = T
And WT + WoT = 2R
or 4WoT = 2R
or R = 2WoT
Total no of houses = T + R = 4WoT + 2WoT = 6WoT
And we have to select a WT from 6WoT.
So the probability = 3WoT/6WoT = 1/2 - So IMO E.
But what are the OAs? Please specify ...
Correct me If I am wrong
Regards,
Amitava
Regards,
Amitava
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ok...look at it this way... you have to pick 2 balls.
now when u pick the first ball.... it may be either 0,1,2 or 3.
If 0 then we need next ball numbered 3 out of 3 balls to sum up as 3...
probability of getting ball with #3 is 1\3
Similarly
If 1 then we need next ball 2 to sum up as 3...
probability of getting ball with #2 is 1\3
Similarly
If 2 then we need next ball 1 to sum up as 3...
probability of getting ball with #1 is 1\3
Similarly
If 3 then we need next ball 0 to sum up as 3...
probability of getting ball with #0 is 1\3
therefore the probablity in either case is 1\3.
now when u pick the first ball.... it may be either 0,1,2 or 3.
If 0 then we need next ball numbered 3 out of 3 balls to sum up as 3...
probability of getting ball with #3 is 1\3
Similarly
If 1 then we need next ball 2 to sum up as 3...
probability of getting ball with #2 is 1\3
Similarly
If 2 then we need next ball 1 to sum up as 3...
probability of getting ball with #1 is 1\3
Similarly
If 3 then we need next ball 0 to sum up as 3...
probability of getting ball with #0 is 1\3
therefore the probablity in either case is 1\3.
ttv wrote: A bowl contains one marble labeled 0, one marble labeled 1, one marble labeled 2, one marble labeled 3. the bowl contains no other objects. If two marbles are drawn randomly without replacement, what is the probility that they willa dd up to 3 ?
(A)1/12
(B)1/8
(C)1/6
(D)1/4
(E)1/3
-thanx
ttv wrote:A housing subdividion contains only 2 types of homes : ranch-style homes and townhomes. There are twice as many townhomes as ranch-homes. There are 3 times as many townhomes with pools than without pools. What is the probability that a home selected at random from the subdivision will be a townhome with a pool ?
Maybe someone will find this method helpful:
2R=T
Probability to pick R is 1/3 and for T is 2/3. They can be T=40 and R=20.
Tp=3Twp Probability to pick Tp is 3/4 and for Twp is 1/4.
Probability to pick T and Tp is 2/3 * 3/4 = 1/2, or if T=40, than Tp is 30 and Twp is 10, and than 30 out of 60 is 1/2
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Hi Camitava, can you explain to me how you get 6 ways when doing 4C2? THANKS!camitava wrote:ttv,
In response to ur first Qs, I would like to take the following approach -
We can get 3 if we chose the following marbles -
(3,0) and (1,2) -> So number of chances = 2
But w/o any condition, we can take 2 marbles out of 4 in 4C2 = 6 ways [Here C -> Combination]
So probability = 2/6 = 1/3
...
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preciousrain7, 4C2 means we taking a combination of 2 out of 4. The formula is - mCn = m!/((m - n)! * n!). Now put m = 4 and n = 2 and u will get 6.
Correct me If I am wrong
Regards,
Amitava
Regards,
Amitava
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THANKS!!!!!!!!camitava wrote:preciousrain7, 4C2 means we taking a combination of 2 out of 4. The formula is - mCn = m!/((m - n)! * n!). Now put m = 4 and n = 2 and u will get 6.
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On the first one, the question says "what is the probility that they will add up to 3"
Don't you think number of favorable cases are [0,1],[0,2][0,3][1,2] which means probability should be 4/6=>2/3..something appears to be incorrect..question/answer choices or my interpretation..
Don't you think number of favorable cases are [0,1],[0,2][0,3][1,2] which means probability should be 4/6=>2/3..something appears to be incorrect..question/answer choices or my interpretation..
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moreonalps, obviously I understood sum up to 3 means only sum of the two marbles will be 3 only! If not, then what u have mentioned is the best way to solve the problem ... TTV, request you to mention the OA. And if u can focus some light on it, please do so ...
Correct me If I am wrong
Regards,
Amitava
Regards,
Amitava
An easy way to solve this problem is plugging in numbers.
Let's consider number of townhouses without pool = 1
With pool = 3 x 1 = 3
Total town houses = 3 + 1 = 4
Ranch houses ( as per the the problem) = 4/2 = 2
Total number of houses = 4+2 = 6
Probability of picking a pool house = 3/6 = 1/2
Let's consider number of townhouses without pool = 1
With pool = 3 x 1 = 3
Total town houses = 3 + 1 = 4
Ranch houses ( as per the the problem) = 4/2 = 2
Total number of houses = 4+2 = 6
Probability of picking a pool house = 3/6 = 1/2