A biased coin with probability , (0 < p < 1) of showing head is tossed until a head appears for the first time. If the probability that the number of tosses required is odd is 7/11 then p =
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am currently stuck with this question, as I prepare for my exam. I'm not sure what kind of answer it is looking for:
A biased coin is tossed until a head appears for the first time. Let p be the probability of head, 0<p<1.
a) What is the probability that the number of tosses required is odd?
b) How about even?
Here's what I have so far:P(1)=pP(2)=(1−p)pP(3)=(1−p)(1−p)pP(4)=(1−p)(1−p)(1−p)pand so on. I understand that it is multiplying by (1−p) for each extra toss. How would I put this in terms of a probability?
A biased coin is tossed until a head appears for the first time. Let p be the probability of head, 0<p<1.
a) What is the probability that the number of tosses required is odd?
b) How about even?
Here's what I have so far:P(1)=pP(2)=(1−p)pP(3)=(1−p)(1−p)pP(4)=(1−p)(1−p)(1−p)pand so on. I understand that it is multiplying by (1−p) for each extra toss. How would I put this in terms of a probability?
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