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Thread: Introductory Statistics/Probability Help

  1. #1
    Maki's Avatar
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    Introductory Statistics/Probability Help


    EDIT: answered but you probably won't see the last of me //flops over
    Last edited by Maki; 04-14-2019 at 12:29 AM.

  2. #2
    Adrieelp's Avatar
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    First of all, I am sorry for my English, it is not my first language, so if you have any questions about the solution or about the steps we take to solve this problem, just ask for clarification, ok?

    Before everything, let's try to understand what the problem asks of us. Your professor wants two events to be independent. What does this strictly mean? It means this:

    P (A ∩ B) = P(A)*P(B)

    Let's try to put this into words. For two events to be independent, the probability of their intersection has to be the product of the individual probabilities. This sounds like gibberish, right? It just means that the probability of A happening has nothing to do with the probability of B.

    Your problem has two probabilities that it wants them to be independent. The probability of someone being Black and the probability of someone being a Woman. It calls event A being a Woman and event B being Black. P(A) is the probability that, if you choose a person at random in this group, it would be a Woman, for instance. P(A) would be like this:

    P(A) = Amount of Women in the group/Total amount of people in the group

    We don't know how many people there are in this endeavor total after we hire black women. We just know how many White Males, Black Males and White Females there are. Let's call the Black Females of X. So:

    Total of people = White Males + White Females + Black Males + Black Females = 50 + 40 + 30 + X = 120 + X
    Total of Women in the group = White Females + Black Females = 40 + X
    Total of Black people in the group = Black Males + Black Females = 30 + X

    P (A ∩ B) means the probability of the intersection of A and B. A is Female and B is Black. So, P (A ∩ B) means the probability of a person of this group being both female and black.

    P (A ∩ B) = Black Females/Total amount of people in the group = X/(120+X)
    P(A) = Amount of Women in the group/Total amount of people in the group = (40+X)/(120+X)
    P(B) = Amount of Black people in the group/Total amount of people in the group = (30+X)/(120+X)

    For this to be independent, this must be truth:
    P (A ∩ B) = P(A)*P(B)

    So, let's substitute the numbers.

    x/(120+x) = [(40+x)/(120+x)]*[(30+x)/(120+x)]
    x/(120+x) = (40+x)*(30+x)/(120+x)�

    Let's multiply the whole equation by 120+x to simplify it.

    x = (40+x)*(30+x)/(120+x)
    120x + x� = 40*30 + x� + 30x + 40x

    Let's subtract x� to both sides of the equation.

    120x = 1200 + 70x
    50x = 1200
    x = 1200/50
    x = 24

    Remember, we called Black Women x. So, there you have it, 24 black women are needed. I am sorry if I sound racist or anything, it is just that the problem uses those terms and I didn't want to confuse you more by renaming the terms. I hope I am of any help.
    Last edited by Adrieelp; 04-14-2019 at 12:10 AM.

  3. The Following User Says Thank You to Adrieelp For This Useful Post:

    Maki (04-14-2019)

  4. #3
    Maki's Avatar
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    Holy shit, you're a god
    +repped handsomely! Is it alright if I possibly tag you in future stats questions tomorrow? This was a wonderful explanation!

  5. #4
    Adrieelp's Avatar
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    Yes, please, I would be glad to help!

  6. The Following User Says Thank You to Adrieelp For This Useful Post:

    Maki (04-14-2019)

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