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
Events A, Band C are mutually exclusive events such that \(P(A) = \dfrac{3x + 1}{3}, P(B) = \dfrac{1-x}{4}\)and \(P(C) = \dfrac{1-2x}{4}\)The set of possible values of x are in the interval
Let A, B be two events in a discrete probability space with ℙ(A) > 0 and ℙ(B) > 0. Which of the following are necessarily true?
For a distribution, the mean is 10, variance is 16, γ 1is + 1 and β 2is 4. The distribution is:
For the discrete distribution, the Pearson's coefficient of skewness β 2is always:
A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ________
