Statistics- probability calculation

Can somebody help me answer the question below please? To be honest, you don't have to necessarily answer it, but if in some way you could show me the correct formulae to use in order to calculate this, that would be really appreciated.

I guess, my main issue around the below, is how to calculate the probability around the or 'a and b' part. Any guidance would be really great.

'Suppose that in a population of people who have worked, the proportion of people who had worked at A last month is 0.20. Also that in the same population, the proportion of people who had worked at B last month is 0.44. The proportion of workers who had worked at both A and B last month is 0.10.'

'What proportion of people in this population had worked at A or B or both last month? '

Reply 1

math42

20

If all else fails on this kind of thing you can draw a Venn diagram but there are appropriate equations
What you desire there is the probability of the union of A and B, P(A U B): this means A or B or both
P(A U B) = P(A) + P(B) - P(A n B) [that should be like an upside down U, not just an n but oh well]

Where P(A n B) is the probability of A and B

Reply 2

alex.kundert

OP

8

Original post by 1 8 13 20 42

If all else fails on this kind of thing you can draw a Venn diagram but there are appropriate equations
What you desire there is the probability of the union of A and B, P(A U B): this means A or B or both
P(A U B) = P(A) + P(B) - P(A n B) [that should be like an upside down U, not just an n but oh well]

Where P(A n B) is the probability of A and B

Cheers! Thanks for the reply :smile:

So, why is it that the union of P(A U B) also includes both? I understand that this would be Probability of A or B, but I do not see how this incorporates 'or both' as well? Hope my question makes sense.........

Reply 3

math42

20

Original post by alex.kundert

Cheers! Thanks for the reply :smile:

So, why is it that the union of P(A U B) also includes both? I understand that this would be Probability of A or B, but I do not see how this incorporates 'or both' as well? Hope my question makes sense.........

Well if you think of A and B as two overlapping circles in a Venn diagram, the probability of their union is the sum of the probabilities in three areas: just A, both A and B and just B.

To show this further, look at P(A U B) = P(A) + P(B) - P(A n B)

P(A) is the probability of "just A" or "A and B", while P(B) is the probability of "just B" or "A and B"

So when we add these together we get "just A" + "just B" + 2 "A and B"

And then Subtracting P(A n B) will give us "just A", "just B" and "A and B"
So the union includes all three regions

Statistics- probability calculation

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