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Binomial probability help

  1. Nov 13, 2011 #1
    A fair coin is tossed 5 times. What is the probability of obtaining exactly 2 heads if it is known that at least 1 head appeared?
     
  2. jcsd
  3. Nov 13, 2011 #2

    mathman

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    Prob(exactly 2 heads)/(1 - Prob(0 heads))
     
  4. Nov 13, 2011 #3
    The way I see it, this is a conditional probability problem that involves the binomial distribution. That is, "what is the probability of getting exactly 2 heads given that at least 1 head occurs".

    The formula for the probabilty of event A given B, written as P(A|B), is:
    P(A|B) = [itex]\frac{P(A\bigcap B)}{P(B)}[/itex].

    In this case, P(A) = probability of exactly 2 heads, and P(B) = probability of ≥ 1 head.
    Since P(A) fulfills P(B) as well, P(A[itex]\bigcap[/itex]B) = P(A)= (10 choose 2)(0.5^5)
    = 0.3125.

    P(B) is a bit trickier. It's basically the P(1 H) + P(2 H) + P(3 H) + P(4 H) + P(5 H), which can also be written as 1 - P(0 heads) = 1 - (0.5)^5 = 0.96875.

    Therefore, P(A|B) = 0.3125 / 0.96875 ≈ 0.323


    EDIT - this is basically the full solution to what mathman just said.
     
  5. Nov 13, 2011 #4
    thanks pshooter that explained so much better!
     
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