A man tosses a fair coin 10 times. Find the probability that he will have: (i) heads on the first five tosses and tails on the next five tosses, (ii) heads on tosses 1,3,5,7,9 and tails on 2,4,6,8,10 tosses, (iii) 5 heads and 5 tails,

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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(a) A man tosses a fair coin 10 times. Find the probability that he will have:
(i) heads on the first five tosses and tails on the next five tosses,
(ii) heads on tosses 1,3,5,7,9 and tails on 2,4,6,8,10 tosses,
(iii) 5 heads and 5 tails,
(iv) at least 5 heads, and
(v) not more than 5 heads.
(b) Consider a binomial random variable ? with parameters ? and ?. Let
? = ?/? be a new random. Show that the expected value of ? is ? and the
variance of ? is ??/?. If ?(?) is the ?. ?. ?. for ?, show that ??~?(?, ?).
What are the possible values that Y can take on?

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