A women-only gym has 60% of its members married. 75% of the married women exercise in the morning and 30% of the single women exercise in the morning. Find the probability of being married if you go to the gym in the morning.

Question

Ultrilliam · Answer

are there any options?

Ultrilliam · Answer

@jhgjg5g

Hero · Answer

@jhgjg5g are you familiar with tree diagrams?

Hero · Answer

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ssddss02 · Answer

Firstly what is 75% of 60%?

ssddss02 · Answer

If 60% of them are married and 75% of those 60% go in the morning just first figure out what 75% of 60% is.

Hero · Answer

You place the appropriate given percentages for members married, members single, married women who exercise in the morning etc.

Then you multiply the set of percentages along each path. There will be four of them:
Let's say:
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What we want to do is find P(A) and P(C), then compute the following:
Probability of being married if you go to the gym in the morning = $\dfrac{P(A)}{P(A) + P(C)}$

Hero · Answer

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BTW, in case anyone was wondering,

$P(A) = 0.6 \times 0.75$
$P(B) = 0.6 \times 0.25$
$P(C) = 0.4 \times 0.30$
$P(D) = 0.4 \times 0.70$