Question

A coin is flipped 5 times, the 1st flip came up heads. What is the conditional probability that exactly 4 heads appeared?

Answer 1

p(F) = “first coin flip comes up heads” = 1/2
This is either heads or tails.
|E ∩ F| = “we get four heads out of five coin flips, and the first flip comes up heads” = C(4, 3).
Assume that the first coin flip is chosen for us, and so we only have r = 3 choices to make from n = 4 items. We then divide by the total number of possible outcomes, 25 .

p(E | F) :- This means that the probability of event E when event F has already occured.
= p(E ∩ F) / p(F)
= (C(4, 3)/25) / (1/2)
= C(4, 3) / 24 = (4!/(3!1!)) / 16
= 4 / 16
= 1 / 4

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