JEE Mains · Maths · STD 12 - 13. probability
An unbiased coin is tossed \(5\) times. Suppose that a variable \(\mathrm{X}\) is assigned the value \(\mathrm{k}\) when \(\mathrm{k}\) consecutive heads are obtained for \(\mathrm{k}=3,4,5\) otherwise \(X\) takes the value \(-1 .\) Then the expected value of \(X,\) is
- A \(\frac{3}{16}\)
- B \(-\frac{3}{16}\)
- C \(\frac{1}{8}\)
- D \(-\frac{1}{8}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{8}\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{c|c|c|c|c|c|c}{\mathrm{k}} & {0} & {1} & {2} & {3} & {4} & {5} \\ \hline P(\mathrm{k}) & {\frac{1}{32}} & {\frac{12}{32}} & {\frac{11}{32}} & {\frac{5}{32}} & {\frac{2}{32}} & {\frac{1}{32}}\end{array}\) Expected value \(=\Sigma \mathrm{XP}(\mathrm{k})\)…
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