May someone please explain how to go about this question ?

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Having independent event we do have

\(P (A & B) = P (A) \times P (B)\)


Now we do know that the LHS is 0.6 as for the stem.

\(0.6= P (A) \times P (B)\)

Now we do also know that the probability is at most 1. We cannot have a probability >1

So we do have for example

A * B in the equation above and suppose that A is 0.3 B must be = 2 to have in the end both 0.6. And this is impossible.

Probability must be equal to 1 at most

IF both the result is 0.6 and B is 0.3 therefore A must be > 0.3 regardless any further calculations

A > B

See more on probability in our handout.

https://gre.myprepclub.com/forum/gre-pr ... tml#p83091
https://gre.myprepclub.com/forum/how-to ... ml#p100949
https://gre.myprepclub.com/forum/how-to ... ml#p100952

Would you please kindly explain why don't we use Venn diagram to solve this problem, but use classic probability?

This is not a n overlapping set question but a question about probability.

Wher did you see overlapping sets ?

I don't see any overlap in the question, but the question doesn't rule out overlap either, so I should be able to assume all possible scenarios, right?

Events A and B are independent. The probability that events A and B both occur is 0.6

Quantity A	Quantity B
The probability that event A occurs	0.3

The question is clearly about probability

Regards

Could this be an alternative solution/ way of thinking?

Since they are independent probabilities

P(AUB) = P(A) + P(B) - Both

P(A)+ P(B) = 1+0.6= 1.6

Max condition: if P(B) is 1 then P(A) is 0.6
Min condition: if P(B) is 0.8 then P(A) is 0.8

Hence P(A) > 0.3