JEE Mains · Maths · STD 12 - 13. probability
A coin is biased so that the head is \(3\) times as likely to occur as tail. This coin is tossed until a head or three tails occur. If \(X\) denotes the number of tosses of the coin, then the mean of \(X\) is
- A \(\frac{21}{16}\)
- B \(\frac{81}{64}\)
- C \(\frac{15}{16}\)
- D \(\frac{37}{16}\)
Answer & Solution
Correct Answer
(A) \(\frac{21}{16}\)
Step-by-step Solution
Detailed explanation
\(P ( H )=\frac{3}{4}\) \(P ( T )=\frac{1}{4}\) \(X\) \(1\) \(2\) \(3\) \(P(X)\) \(\frac{3}{4}\) \(\frac{1}{4} \times \frac{3}{4}\) \(\left(\frac{1}{4}\right)^3+\left(\frac{1}{4}\right)^2 \times \frac{3}{4}\)…
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