probability

Question

I am fine with (a)...which is 1/3....i am not able to understand b) and c) ....i feel answer as same for all 3 ...but answer given is different ....can anybody tell the difference between a) and b),c)

Comments

I alsp found same results for all

Answer 1

problem c) is trivial ...chances of getting a HHT in 3 flips of an unfair coin is 0 ...because unfair coin always gives a H not T 

Answer 2

(a)

$\begin{align*} &(a) \\ &\text{Required probability} = \frac{0.5*0.5}{0.5*0.5+0.5*1} = \frac{1*0.5^2}{1*0.5^2+0.5} = \frac{1}{3} \\ \\ \hline \\ \end{align*}$

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(b)

$\begin{align*} &(b) \\ &\text{Required probability} \\ &=\frac{0.5*0.5*0.5 + 0.5*0.5*0.5 }{0.5*0.5*0.5+0.5*0.5*0.5+0.5*1*1} \\ &= \frac{2*0.5^3}{2*0.5^3+0.5} \\ &= \frac{0.5^2}{0.5^2+0.5} \\ &= \frac{1}{3} \\ \\ \end{align*}$

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(c)

$\begin{align*} &(b) \\ &\text{Required probability} \\ &=\frac{4*0.5*0.5*0.5*0.5}{4*0.5*0.5*0.5*0.5+0.5*1*1*1} \\ &= \frac{4*0.5^4}{4*0.5^4+0.5} \\ &= \frac{0.5^2}{0.5^2+0.5} \\ &= \frac{1}{3} \\ \\ \end{align*}$.