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There are two misshapen coins in a box; their probabilities for landing on heads when they are flipped are, respectively

Posted: Wed May 11, 2022 9:32 am
by answerhappygod
There are two misshapen coins in a box; their probabilities for
landing on heads when they are flipped are, respectively, .4 and
.7. One of the coins is to be randomly chosen and flipped 10 times.
Given that the two of the first three flips landed heads, what is
the conditional expected number of heads in the 10 flips?