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# Mary Kate is describing potential relationships between one having a military veteran status and an optimistic outlook on the economy.

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Mary Kate is describing potential relationships between one having a military veteran status and an optimistic outlook on the economy. Assume a survey of 401 randomly selected persons revealed the following data:

The probability of selecting a person with no military veteran status is 0.926.

If a person with no military veteran status is chosen, the probability they have a pessimistic outlook on the economy is 0.582 and if a person with a military veteran status is chosen, the probability they have an optimistic outlook on the economy is 0.567

If you were to choose a person at random from the sample, determine the probability they have a military veteran status given that they have an optimistic outlook on the economy.

Let's suppose that 1,000 people were surveyed rather than just 401.

Number(no military veteran status) = 926

Number(no military veteran status and a pessimistic outlook on the economy) = 582

Number(a military veteran status and an optimistic outlook on the economy) = 567

So...

Number of no military veteran status only = 926 - 567 = 359

Number of no military veteran status and a pessimistic outlook on the economy only = 582 - 567 = 15

Number of military veteran status and an optimistic outlook on the economy = 1,000 - (359 + 15 + 567) = 1,000 - 941 = 59

P(a military veteran status and an optimistic outlook on the economy) = 59/1000 = 0.059?

(This is my attempt to solve a similar problem, so I hope someone can check my work if I did it correctly or not.)

Dec 21, 2020

#1
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I think this one is a LEEEETLE  bit different thatn the others posted so far

1000 people    926   no military   so   74 military

out of 74 military    .567 are optimistic     74 * .567 = ~42 folks with military and optimistic

( 42 out of 1000 are + military and opt )

No military is 926     pessimistic is .582 of this    926(.582) = ~ 556 <=====  the rest are no military and optimistic = 926-556 = 370

SO total optimistic is   370 + 42 = 412   optimistic people

42 out of 412    would be the optimistic with military hx = .102         (I hope I didn't steer you wrong on this one !)

Venn diagram to follow...........

Dec 21, 2020
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**** edit ****

I think this one is a LEEEETLE  bit different thatn the others posted so far

1000 people    926   no military   so   74 military

out of 74 military    .567 are optimistic     74 * .567 = ~42 folks with military and optimistic

( 42 out of 1000 are + military and opt )

No military is 926     pessimistic is .582 of this    926(.582) = ~539 <=====  the rest are no military and optimistic = 926-539 = 387

SO total optimistic is  387+ 42 = 429   optimistic people

42 out of 429  would be the optimistic with military hx = .0979       (I hope I didn't steer you wrong on this one !)

Venn diagram to follow...........

Guest Dec 21, 2020
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So my first answer was incorrect for not knowing that this problem takes a different approach to solving it. Right then, I will look at this over to learn my mistakes and try again. Thanks again for your efforts, my fellow user!

GAMEMASTERX40  Dec 21, 2020
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Venn diagram

Dec 21, 2020
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These questions are not worded properly.

I mean this question and at least one other similar question that you have posted.

Dec 22, 2020