Please solve this Q from CL - FLT

[amit_in1976]

Hi,
Following is a question from CL - FLT (mycase it is FLT-9 from last year's material).

A shop has two different types of utensils - 6 of type A and 4 of type B. There are three customers who visit this shop and each of them buys 1 utensil. What is the probability that more than two utensils of type A are purchased.

The answer is 1/2 and the explanation given is not convincing.

My solution would be 6C2*4C1+6C3/10C3 which comes to 2/3


Also, another question from the same FLT

What is the difference between the smallest 4 digit Hexadecimal no and largest 4 digit hexadecimal no.

My answer is FFFF-0000 = FFFF

The solution says FFFF-1000=EFFF

Please let me know where I am wrong?

[zango]

For the first problem, i think 1/2 is correct. See, i think this is not a biased selection (meaning if you have 6 of type A, it doesn't increase chances of A getting selected over B). Since there are more than 3 utensils of each type, a customer can choose any one of the utensils (irrespective of number of utensils available).

So - i chart it out: as follows
if X,Y,Z are the three customers.
then
X Y Z
A A A
A A B
A B A
A B B
B A A
B A B
B B A
B B B

Now, if you were to count the number of total cases - and the number of cases in which there are 2 A's, you will see the desired probability = 4/8 = 1/2. Please let me know if this is the same way CL has shown in their FLT soln


I am not very sure about this one - but i guess by 4 digit they mean the first digit should be non-zero. This is an instance of the ambiguous wording - that I have been facing a lot in CL mocks - (okay it is not so ambiguous - the questions i really get confused with - man i should post an instance of that - I hope CAT doesn't have ambiguity in the questions).

hth.
Cheers!

[chiclets]

I dunno abt the first one,your ans seems just fine.
in the 2nd one 0000 isnot the first 4 digit hex number,,,
tahst like saying 0000 or 0001 is the first 4 digit natural number.
while actually the 1st 4 digit hex number is 1000
so voila

[varsha]

A shop has two different types of utensils - 6 of type A and 4 of type B. There are three customers who visit this shop and each of them buys 1 utensil. What is the probability that more than two utensils of type A are purchased.

Am I missing something here.
More than two utensils of type A
There is only one case then shouldn't the answer be 1/8

Correct me if I am wrong
Varsha

[makl]

Dear Frend,

I think the answer to the first question would be this:

In all only 3 utensils have been purchased (more than 2 purchased and each person has bought only 1 utensils, that leads us to the number 3). Now there are only four ways in which the items could be purchased:

1) B-0, A-3
2) B-1, A-2
3) B-2, A-1
4) B-3, A-0

Only option 1 meets our requirement as per the question, out of the 4 options. Hence, the probability of more than 2 utensils (i.e. 3 in fact) of type A being bought is 1/4.

hope the answer is correct.

in case u have any other opinion pls let me know at my mail ID makl@rediffmail.com

bye!!!

[zango]

Originally Posted by varsha @ Thu Oct 28, 2004 3:08 pm

Am I missing something here.
More than two utensils of type A
There is only one case then shouldn't the answer be 1/8

Correct me if I am wrong
Varsha

I didn't realize it said more than 2 - i thought it read 2 or more.
i guess we will have to wait for the original poster to clarify.

[ronjan]

Hi ,

interesting thread , good Old cat days )

Here is my take

1) We have to find the probability that the three customers buy either 2 or 3 utensils of type A

Each customer can buy an utensil in 2 ways because each customer irrespective of his entrance order in the shop will have 2 choices - Buy A or B *This is because the no. of utensils of either type is > 2, hence none of the choices is finished*.

Hence , P(A = 3) = (1/2)^3 = 1/8
and P(A=2) = (3C2)*(1/2)^3= 3/8

Hence, reqd. probability = P(A=2)+P(A=3) = 1/2.

2) Remember, class 7 mathematics ? smallest 4-digit no. was always 1000 not 0000 same funda .

Best wishes
ranjan

[amit_in1976]

Zango/Varsha,
The first statement of the question says that all the three customers have bought 1 utensil each. So if the calculation is for 2 or more of type A, this means that two customers or all customers buy utensils of type A.

The solution given by Zango is the one mentioned in CL FLT. However, I feel that solution given by Ranjan seems more mathematical.

For the second one, Ranjan I had initially thought about the same that if we say four digits, then it is 1000 but then in many problems I have seen...0000 is also considered a case. Maybe I am confused!

Thanks for the help anyways.

Regards

[ronjan]

Mod delete this plz , was a double post...sorry !!!

[ronjan]

Originally Posted by Amit

I have seen...0000 is also considered a case.

Possible, but personally the 2-3 qns i can recall *and maybe i am wrong*, 0 was never a consideration.

Anyways dont focus too much on the answer-keys; if u believe ur fundae are correct; nothing like dat .

Cya
ronjan