Probability question
- From: "Tadeusz Jordan" <tedjj@xxxxxxxxxxxxxx>
- Date: Mon, 30 Apr 2007 17:45:03 -0400
Hello. I'm preparing for the test tomorrow and I got stuck on this problem.
When coin 1 is flipped, it lands heads with probability .4; when coin 2 is
flipped, it lands heads with probability .7. One of these coins is randomly
chosen and flipped ten times.
(a) What is the probability that exactly 7 of the 10 flips land on heads?
(b) Given that the first of these ten flips lands head, what is the
conditional probability that exactly 7 of the 10 flips land on heads?
I solved part (a) 1/2 * (10 choose 7) * .4^7 * .6^3 + 1/2 * (10 choose 7) *
..7^7 * .3^3
I'm having problems with part (b). I denoted E as the event that there will
be exactly 7 heads and F that 1st lands heads. So P(E|F) = P(EF)/P(F)
P(F) = 1/2 * .4 + 1/2 * .7 = .55
Can anyone tell me how to calculate P(EF) ?
Tadeusz Jordan
.
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