At the moment, we're comparing the following:
QUANTITY A: 0.11/d
QUANTITY B: 0.09

Let's test some possible values of d.

If d = 1, then we get:
QUANTITY A: 0.11/d = 0.11/1 = 0.11
QUANTITY B: 0.09
In this case, Quantity A is greater


If d = 0.7 then we get:
QUANTITY A: 0.11/d = 0.11/0.7 ≈ 0.157
QUANTITY B: 0.09
In this case, Quantity A is greater


If d = 0.5, then we get:
QUANTITY A: 0.11/d = 0.11/0.5 = 0.22
QUANTITY B: 0.09
In this case, Quantity A is greater


If d = 0.25, then we get:
QUANTITY A: 0.11/d = 0.11/0.25 = 0.44
QUANTITY B: 0.09
In this case, Quantity A is greater


If d = 0.1, then we get:
QUANTITY A: 0.11/d = 0.11/0.1 = 1.1
QUANTITY B: 0.09
In this case, Quantity A is greater

So, since 0 < d ≤ 1, we can be certain that Quantity A is greater

Righht!! my bad..thanks so much.

I know I did something really wrong here, but I can't figure out why we can't write the equation as this.

While solving this question for the first time, I wrote this.

What is wrong with this approach? Doesn't the equation above explain independent probabilities?

This is more logic than an equation to be frank

C * D = 0.11

To have at least 0.11 C cannot be as low as 0.9. Must be greater

So C > 0.9

A is the answer

Can’t it be possible that
Both probabilities are 0.055
As 0.055*0.055= 0.11
And p(c) is less than 0.09
Another, 0.11
It varies so D ???
Qn isn’t saying min/max so how can we consider p(d)=1 only it could be anything

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Carcass can this question be solved this way?
is this approach right?
probability of both C and D of happening = 0.11
probability of both events not happening is = 0.89
1 - .89*.89 = (Approx 0.2)
QA>QB

Another way is to use Quantity B as a benchmark value.

P(C)*P(D) = 0.11

Therefore, P(D) = \(\frac{0.11}{P(C)}\)

Now, assume P(C) = Quantity B = 0.09

then, we get

P(D) = \(\frac{0.11}{0.09} = 1.222222\)

P(D) cannot be greater than 1.

Therefore, P(C) cannot even be equal to 0.09 (Quantity B), it has to be always more than Quantity B.

Hence Quantity A is the answer.

The problem talks about two independent events occurring together. The formula is \(P(C) \times P(D) \)

Your formula applies for two independent events, that are not mutually exclusive, where only one OR the other occur. The formula is \(P(C or D) = P(C) + P(D) - P(C and D)\)

well i got the simplest way to solve this

just divide 0.11 by 0.09
and you'll get 1.22 which is obvious wrong as we know the probability can never be greater than 1
so C cannot be 0.09 but a number much bigger than 0.09 and hence Option A is correct