Consider an experiment such that we flip a coin until the first time a heads is...
Consider an experiment such that we flip a coin until the first time a heads is observed. Let E be the event that the first time a heads turns up is on an odd numbered flip (so we get a heads on our 1st, 3rd, or 5th flip and so forth). What is the probability that E occurs?
Homework Answers
P(E) = P(first head on 1st flip) + P(first head on 3rd flip) + P(first head on 5th flip) + ....
= 0.5 + P(tail)2 * P(head) + P(tail)4 * P(head) + ...
= 0.5 + 0.53 + 0.55 + ....
= 0.5 / (1 - 0.52)
= 0.667 (ans)
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