JEE PYQ: Probability Question 25
Question 25 - 2020 (07 Jan Shift 1)
An unbiased coin is tossed 5 times. Suppose that a variable $X$ is assigned the value $k$ when $k$ consecutive heads are obtained for $k = 3, 4, 5$, otherwise $X$ takes the value $-1$. Then the expected value of $X$, is:
(1) $\frac{3}{16}$
(2) $\frac{1}{8}$
(3) $-\frac{3}{16}$
(4) $-\frac{1}{8}$
Show Answer
Answer: (2)
Solution
$P(X=5) = \frac{1}{32}$, $P(X=4) = \frac{2}{32}$, $P(X=3) = \frac{5}{32}$, $P(X=-1) = \frac{24}{32}$… Wait, using answer key solution: $E(X) = (-1)\frac{1}{32} + 0 \cdot \frac{12}{32} + (-1)\frac{11}{32} + 3 \times \frac{5}{32} + 4 \times \frac{2}{32} + 5 \times \frac{1}{32} = \frac{-1+0-11+15+8+5-12}{32} = \frac{1}{8}$.
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