If three numbers are randomly selected from set A without

Question

Set A: {1, 3, 4, 6, 9, 12, 15}

If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3?

A. 3/14
B. 2/7
C. 9/14
D. 5/7
E. 11/14

The sum of any three number from set B={3,6,12,15} would be divisible by 3. with combination method we can find how many ways we can select 3 numbers from set B. 5C3 = 10 so the probability would be  10/7

2nd method is of probability: The easy would be not selecting 1 and 4 from the set.
so P(not 1 and not 4) = P (not 1) * P(not4) => (1-1/7) * (1-1/6) =>  5/7

Both Answers are wrong !!
 where i'm going wrong.
Thanks

Bunuel · Accepted Answer

Set A: {1, 3, 4, 6, 9, 12, 15}

If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3? 
A. 3/14
B. 2/7
C. 9/14
D. 5/7
E. 11/14

How can the probability be more than 1?

Probability of an event = (# of favorable outcomes) / (total # of outcomes).

There are 5 numbers you can choose from (3, 6, 9, 12, 15) so that the sum to be divisible by 3 and there are total of 7 numbers so  P=\frac{C^3_5}{C^3_7}=\frac{2}{7} .

Answer: B.

shrive555 · Answer

ooo... i'm so dumb !! the denominator with 7C3. choosing 3 out of 7
but whats wrong with the 2nd method ?

Bunuel · Answer

I'm not sure what are doing in your second approach but using probability you can solve: 5/7*4/6*3/5=2/7.

PiyushK · Answer

sum of 3 multiples of 3 is divisible by 3.
sum of 2 multiples of 3 with one non multiple of 3 will never be divisible by 3.
sum of 1 multiple of 3 with 2 non multiples is only possible if sum of two non multiples is divisible by 3.

1,3,4,6,9,12,15
1 and 4 are non multiple.

5C3 ways to select multiples of 3.

4+1 = 5 thus third possibility one multiple of 3 with 2 non multiple is not possible.

Therefor 5C3/7C3 = 2/7 ans.

JusTLucK04 · Answer

You can Get a multiple of 3 by adding multiples of 3 only...(Unless you have repeat numbers such as three 2's or 5 1's)

5 multiples of 3..
5C3

Total possible combinations
7C3

= 2/7

KJA · Answer

Bunuel  how about reverse probability? this is what i tried and ended up with the wrong answer:  1-\frac{2}{7}*\frac{1}{6}*1+\frac{2}{7}*\frac{5}{6}*\frac{4}{5}= 1-\frac{5}{21}

Poorvasha · Answer

No of ways of selecting 3 numbers out of the total of 7 numbers = 7C3
5 out of the total set of 7 numbers are multiples by 3 and hence, will account to the sum being divisible by 3 = No of ways of selecting favorable outcome = 5C3

P(E) - 5C3/ 7C3 = 2/7 (B)

spetznaz · Answer

The required probability is (5c3/7c3). The answer comes to 2/7. Option B it is !

harsh8686 · Answer

Hi  Bunuel ,

If we want to do another way => 1 - P(choosing 1 and 4)

then as per the number of ways to chose 1 and 4 = (1,4,3), (1,4,6), (1,4,9), (1,4,12), and (1,4,15); in short 5C1

therefore P(choosing 1 and 4) should be = 5/(7c3) = 5/35 = 1/7
and P(NOT choosing 1 and 4) should be = 1-1/7 = 6/7

What I am doing wrong?

Bunuel · Answer

You are missing cases there. What about: {1, 3, 6}; {1, 3, 9}; {1, 3, 12}; {1, 3, 15}; {1, 6, 9}; {1, 6, 12}; {1, 6, 15}; {1, 9, 12}; {1, 9, 15}...

nisthagupta28 · Answer

Please check if my method is correct.

For the sum to be divisible by 3, the individual term has to be a multiple of 3. 1 and 4 if added to other terms or added to each other will not be divisible by 3. 
So we have only 5 favourable outcomes.

Probability of picking 1 st number - 5/7
Probability of picking 2nd number - 4/6
Probability of picking 3rd number - 3/5
(because it is without replacement)

Since, it is P(1) and P(2) and P(3) i.e. the same as P(1) * P(2) * P(3)

so. 5/7 * 4/6 * 3/5 = 2/7

karnavora1 · Answer

There are 5 numbers in the set that are divisible by 3 which are 3,6,9,12,15

We are asked to pick 3 numbers without replacement hence the probability will be

\frac{5}{7}*\frac{4}{6}*\frac{3}{5}=\frac{2}{7}

Since we are removing without replacement with each number we pick we should reduce the numerator and denominator by 1.

Answer is  \frac{2}{7}

Abhipsa20 · Answer

Just curious to know the 10 possible combinations
3,6,9
3,6,12
3,6,15
3,9,12
3,9,15,
3,12,15
6,9,12
6,9,15
9,12,15
Which is the one I am missing?

Greg1234 · Answer

I understand using combinations to solve the answer: 7C3 total combinations, and 5C3 cases where the sums of three numbers are divisible by 3. However I also considered that choosing one 4 and two ones results in a number divisible by 3. I was wondering if my interpretation of the question is incorrect, as in does no replacement also suggest no repetitions or should I just inherently assume that any number cannot be selected twice. I appreciate any clarification.

Bunuel · Answer

We are given a set and we are choosing numbers from it without replacement. In the problem, "without replacement" means each number from set A can only be chosen once. So, you cannot select '1' or '4' twice.

bumpbot · Answer

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