If two numbers, a and b, are to be chosen from a set of 4

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if the question is modified by taking out the word 'respecitively' from this question, how would one approach it?

{1,2,3,4}
{4,6,8}
b/a not integer 4/3,6/3,8/3
p = 3/12 =1/4

If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 4, respectively, what is the probability that b/a will not be an integer?

Answers:
(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3

Soln:
a is from the following set {1,2,3,4}
b is from the following set {4,6,8}

Total number of ways of choosing 2 integers, one from each set is = 4* 3 = 12 ways

Now the number of possibilities where b/a is not an integer is for the following outcomes
{b,a} => {4,3},{6,4},{8,3} = 3 ways

Hence probability is = 3/12 = 1/4

ans is B

Hey suresh,

you probably meant:
b/a not integer 4/3,6/4,8/3

OK, here's an example of how to get an easy question wrong.
I assumed (misread) the question to mean that a and b sets are interchangeable.
Implying that a and b could be selected from either {1,2,3,4} or {4,6,8}.

I now realize that I had misread the question, but if that was the original question, then:
P(b/a is not an integer)
= P(b/a not an integer where b in {1234} and a in {468})
+ P(b/a not an integer where b in {468} and a in {1234})
= 11/12 + 3/12
= 7/12.

Going back to the question that was asked:
P(b/a not an integer where b in {468} and a in {1234})
= 3/12
= 1/4.

In such problems, it is better to first write down all the cases that are in cosideration

Set A = {1, 2, 3, 4}
Set B = {4, 6, 8}

Total outcomes: 4*3 = 12

Favourable outcomes:
We need B/A, hence considering one element of the set B at a time

4: only 3 satisfies our condition (4 is divisible by 1, 2 and 4)
6: only 4 satisfies our condition (6 is divisible by 1, 2 and 3)
8: only 3 satisfies our condition (8 is divisible by 1, 2 and 4)

Favourable outcomes = 3
Probability = 3/12 = 1/4
Option B

a relatively easy question that can be solved by enumerating all the outcomes:
1st list: 1, 2, 3, 4
2nd list: 4, 6, 8

now, possible options:
4/1
4/2
4/3 - non-integer
4/4

6/1
6/2
6/3
6/4 - non-integer

8/1
8/2
8/3 - non-integer
8/4

total 12 outcomes, out of which 3 are "successful" outcomes. 3/12 = 1/4

Am I the only one who interpreted the question in the following manner?

Given that the first set consists of 4 consecutive integers starting with 1, I assumed the set will be something like this {10, 11, 12, 13} or {102,103,104,105} and same for the second set {404, 406, 408}. This made me lose my mind on how to go about

You are not. The question is worded poorly.

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