The expected number of trials for first occurrence of a “head” in a biased coin is known to be 4. The probability of first occurrence of a “head” in the second trial is _____________ (Round off to 3 decimal places).
By Geometrical distribution,
\(E(x) =\frac{1}{P} \)
\(V(x) =\frac{q}{P^2} \)
\(E(x) =4=\frac{1}{P} \)
\(q =1-\frac{1}{4}=\frac{3}{4} \)
\(P(H) =\frac{1}{4}, \)
\(P(T) =\frac{3}{4}\)
Required probability, P(E) = P(T H)
= \(\frac{3}{4} \times \frac{1}{4}=\frac{3}{16}=0.1875\)
Important Questions from Basics of Probability
If the data are skewed, which option of central tendency measure is the most unreliable indicator?
In a negatively skewed distribution
If the distribution is negatively skewed, then the:
The first four moments about the mean of distribution are 0, μ 2, 0.7 and 18.75. If the distribution is mesokurtic, the value of μ 2, is
If Mean > Median > Mode, the distribution is:
