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  1. #1
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    Basic Probability Help

    The question says 4% of people of watch American Idol. In a group of 3 randomly selected people, what is the probability that at least two of them watch American Idol?

    how do I start this? we just learned this yesterday so i am new at this.. and i am very confused. if anyone could explain to me how to do, that would be great. thank you so much.

    -----------------

    got a question here too..



    1) Why does P(A and Complement of B) = 4/18?
    2) Why does P(A or Complement of B) = 13/18?

    i got some questions about that because for #1, why do you not count the middle 3 dots that they share? Cause in #2 you count them for some reason. As for #2, why do you count the outside dots as well, and why do you count the middle 3 dots?
    Last edited by mneox; December 12th 2009 at 02:25 PM.
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  2. #2
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    Hello mneox
    Quote Originally Posted by mneox View Post
    The question says 4% of people of watch American Idol. In a group of 3 randomly selected people, what is the probability that at least two of them watch American Idol?

    how do I start this? we just learned this yesterday so i am new at this.. and i am very confused. if anyone could explain to me how to do, that would be great. thank you so much.
    First an administrative note: in future, post each question as a separate thread. (See rule 14.)

    If we choose a group of n people, then to find the probabilities of each number from 0 to n watching AI we use the Binomial Distribution formula. This says that the probability that exactly r of them watch AI is:
    p(r)=\binom{n}{r}p^r(1-p)^{n-r}
    where p is the probability that any given person chosen at random watches AI.

    So here, n=3, p=\frac{4}{100}=0.04, and 1-p=0.96. So we need to find p(2) and p(3) and add them together. I'll start you off:
    p(2) = \binom32\times0.04^2\times0.96=0.004608
    Can you complete it? (I make the final answer 0.004672.)
    -----------------
    got a question here too..



    1) Why does P(A and Complement of B) = 4/18?
    2) Why does P(A or Complement of B) = 13/18?

    i got some questions about that because for #1, why do you not count the middle 3 dots that they share? Cause in #2 you count them for some reason. As for #2, why do you count the outside dots as well, and why do you count the middle 3 dots?
    You need to understand what intersection, \cap, and union, \cup, mean in set theory. So read what I'm saying here really carefully.

    The set (A and complement of B) - which is denoted variously by A \cap B' or A \cap \bar{B} or A \cap B^C - is the intersection of the set A with the set B'; that is, the set of elements that are in A but not in B.

    So p(A \cap B') means the probability that a dot chosen at random is inside loop A but not inside loop B. There are four dots in this region, out of a total of 18 dots. So the probability of this is \frac{4}{18}.

    The set (A or complement of B)- which is A \cup B' (or ... etc) - is the union of set A with set B'; that is, the set of elements that are in A or not in B. The only elements that will be excluded from this set, then, are those that are in B but not in A. There are just 5 of these in the diagram; the remaining 13 are in A\cup B'. So the probability that a dot chosen at random is in this set is \frac{13}{18}.

    Grandad
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