A bag contains 15 wool scarves, exactly one of which is red and exactl

Question

A bag contains 15 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and draws three scarves, simultaneously and at random, what is the probability that she selects the red scarf but not the green scarf?

a) 2/35
b) 1/15
c) 6/35
d) 13/70
e) 1/5

a) 2/35
b) 1/15
c) 6/35
d) 13/70
e) 1/5

EMPOWERgmatRichC · Accepted Answer

Hi ynaikavde,

The "math" behind this question can also be handled as a Permutation. Here's how:

We have 15 scarves: 1 red, 1 green and 13 other. We're asked for the probability of grabbing 3 scarves that include the 1 red but NOT the 1 green scarf.

Even though the question states that we are supposed to grab all 3 scarves simultaneously, we can still refer to them as 1st, 2nd and 3rd. There are 3 ways to get what we *want*

R = Red
O = Other

ROO
ORO
OOR

The probability of getting ROO = (1/15)(13/14)(12/13) = 2/35

The probability of getting ORO = (13/15)(1/14)(12/13) = 2/35

The probability of getting OOR = (13/15)(12/14)(1/13) = 2/35

Total ways = 2/35 + 2/35 + 2/35 = 6/35

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

So, we need 1 red out of 1, and 2 (some other color but red and green) out of 13.

P = \frac{C^1_1*C^2_{13}}{C^3_{15}}=\frac{78}{455}=\frac{6}{35} ,

Answer: D.

aamirnawaz · Answer

Ans- C

Sample space=  15C3 
No. of possible outcomes when one red scarf to be selected and green scarf is not to be selected=  13C2

Required probability =  \frac{13C2}{15C3} 
 =  \frac{(13*6)}{(5*7*13)} 
 =  \frac{6}{35}

damyanti · Answer

Probability = number of favorable outcomes/total number of possible outcomes

Total number of possible outcomes = C(15,3)

Number of favorable outcomes = Number of ways in which one red scarf and two non-green scarves can be drawn
Number of favorable outcomes = 1*C(13,2)

This is because there is only one way in which one red scarf can be drawn, while there are C(13,2) ways in which two non-green scarves can be drawn, because we have to draw any two out of the 13 remaining (since red one is already drawn and green one we don't have to draw).

So, probability = C(13,2)/C(15,3)=6/35

dina98 · Answer

You mean C, correct?

adiagr · Answer

Theory:

To Find Probability when a red scarf is chosen but a green scarf is not chosen. 
First Find probability when Red scarf is necessarily chosen. say this is (1)
Then Find Probability when both of them are chosen together. Say this is (2) 
(1) - (2) will give the probability when Red is chosen but Green is not chosen

Probability of selecting 3 scarves such that a Red scarf is necessarily selected P(R)
=  \frac{14C2}{15C3}  (We always choose the red scarf, no restrictions on other two)
= ( \frac{14!}{12!2!} ) divided by ( \frac{15!}{12!3!} )
 =  \frac{14!12! 3!}{12!2! 15!}  
=  \frac{3}{15}  
=  \frac{1}{5}

Probability of selecting 3 scarves such that One of them is Red and One is a Green scarf 
=  \frac{13C1}{15C3}  (We choose the red scarf, We choose the green scarf, then out of remaining 13 we choose remaining 1 scarf) 
 = ( \frac{13!}{12!} ) divided by ( \frac{15!}{12!3!} )
 =  \frac{13!12! 3!}{15!12!}  
=  \frac{13!3!}{15!}  
=  \frac{6}{15*14}  
=  \frac{1}{35}

Now we have to find the Probability that a Red Scarf is selected but a Green scarf is not selected.

This will be  
=  \frac{1}{5}  -  \frac{1}{35}  
=  \frac{7}{35}  -  \frac{1}{35}  
 =  \frac{6}{35}

C is the answer.

Vibhatu · Answer

Bunuel  please mention whether it is with replacement or without replacement

Posted from my mobile device

Bunuel · Answer

The word "simultaneously" indicates that all scarves were drawn at the same time, so no replacement there.

Vibhatu · Answer

Thank you for your confirmation  Bunuel . thankyou for your help!!

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A bag contains 15 wool scarves, exactly one of which is red and exactl

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