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High school conditional probability

  1. Jan 18, 2012 #1
    Two coins are flipped and the results are recorded. Given that one coin lands on a head, find the probability of:

    a) Two heads, b) a head and a tail

    Searching online is giving my answers which are not using conditional probability at all, and our teacher told us we have to use the formulas etc, but i keep getting it incorrect.

    Well i haven't attempted b as i can't do a but here is my working:

    Let a be the coin that lands on heads
    Let b be the unknown coin

    so P(B | A) = P(B and A) / P(A)

    P(A) = 1/2
    P(B) = 1/2

    P(B and A) = 1/4

    P(B | A) = 1/4 / 1/2 = 1/2 which is obviously wrong.

    To be honest i think P(A) is correct but i don't know how to do P(B).
  2. jcsd
  3. Jan 18, 2012 #2


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    Let A be event either coin lands on head.

    For a. let B be the event both coins land on heads,
    P(A)=3/4, P(B)=1/4, P(B|A)=(1/4)/(3/4)=1/3. Note that A ∩ B = B

    For b. Let B' be the event that one coin is heads and the other is tail.
    P(A)=3/4, P(B')=1/2, P(B'|A)=2/3. Here A ∩ B' = B'
  4. Jan 19, 2012 #3


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    Clarification: B' is NOT the complement of B in this example.
  5. Jan 19, 2012 #4

    thank you for your response i cleared it up with my teacher today though i still have a question on how to get P(AnB), why is it = to B? I thought the formula for P(AnB) = P(A) + P(B) - P(AuB), but how do you get p(AuB).

    Thank you.
  6. Jan 19, 2012 #5
    In this case, we have that [itex]B\subseteq A[/itex]. Indeed: if both coins land on head, then one of the coins lands on head.
  7. Jan 19, 2012 #6
    I'm sorry but what is that symbol, we haven't learnt it yet.
  8. Jan 20, 2012 #7


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    "subset". The set B= {hh} (both heads) is a subset of A= {hh, ht, th} (at least one head).
  9. Jan 20, 2012 #8


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    Since B is a subset of A, the intersection is B and the union is A.
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