An unfair coin having probability of showing Head p is flipped 6 times. Assume t

Question

An unfair coin having probability of showing Head p is flipped 6 times. Assume that all the tosses are independent.

(a) What is the probability that the coin will show Head 4 times and Tail 2 times?

(b) What is the probability that the coin will show at least 1 Head in the first 4 tosses?

(c) Assume that there was no Head in the first 4 tosses, what is the probability that the coin will show Head for the first time at the 6th toss?

(d) Find the probability to get second Head at the 5th toss.

Please show me how you derive the answer step by step.

Explanation / Answer

let's call (1-p) = q

a.6c4*p^4q^2

b.1 - q^4

c. qp [ remember, probability has no memory ]

d. 4c1*p*q^3 *p = 4p^2q^2

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