Suppose that a fair coin is tossed repeatedly and independently. Let ‘ $X$ ’ denote the number of tosses required to obtain for the first time a tail that is immediately preceded by a head. Then $E (X)$ and $P (X > 4)$ , respectively are

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$6 and \frac{11}{16}$

$4 and \frac{11}{16}$

$6 and \frac{5}{16}$

$4 and \frac{5}{16}$

answer is A.

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Detailed Solution

$\begin{array}{lll} X = 2 & HT & \frac{1}{4} \end{array}$

$X = 3 THT \frac{2}{8}$

$HHT$

$X = 4 TTHT$

$THHT$

$HННТ \frac{3}{6}$

$E = \sum_{n = 1}^{σ} \frac{(n + 1) n}{{4.2}^{n - 1}} = 4$

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