A candidate takes three tests in succession a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $S$ denote success (pass) and $F$ denote failure (fail). The probability of passing the first test is $P(S_1) = p$,so $P(F_1) = 1-p$.For subse

Vedclass · Accepted Answer

$p^2(2-p)$

Vedclass · Answer

(A) Let $S$ denote success (pass) and $F$ denote failure (fail). The probability of passing the first test is $P(S_1) = p$,so $P(F_1) = 1-p$.For subsequent tests,$P(S_{n+1} | S_n) = p$ and $P(S_{n+1} | F_n) = \frac{p}{2}$.The candidate is selected if they pass at least two tests. The possible favorable outcomes are:$1$. Pass $I$,Pass $II$,Fail $III$: $p 	imes p 	imes (1-p) = p^2(1-p)$$2$. Pass $I$,Fail $II$,Pass $III$: $p 	imes (1-p) 	imes \frac{p}{2} = \frac{p^2(1-p)}{2}$$3$. Fail $I$,Pass $II$,Pass $III$: $(1-p) 	imes \frac{p}{2} 	imes p = \frac{p^2(1-p)}{2}$$4$. Pass $I$,Pass $II$,Pass $III$: $p 	imes p 	imes p = p^3$Summing these probabilities:$P = p^2(1-p) + \frac{p^2(1-p)}{2} + \frac{p^2(1-p)}{2} + p^3$$P = p^2(1-p) + p^2(1-p) + p^3$$P = 2p^2 - 2p^3 + p^3 = 2p^2 - p^3 = p^2(2-p)$.

Similar Questions

Which of the following salts does not give a flame test?

$0.16 \ g$ of an organic compound containing sulphur produces $0.233 \ g$ of $BaSO_4$. The percentage of sulphur in the compound is:

If $f(x) = \begin{cases} \frac{\sin(1+[x])}{[x]}, & \text{for } [x] \neq 0 \\ 0, & \text{for } [x] = 0 \end{cases}$ where $[x]$ denotes the greatest integer not exceeding $x$,then $\lim_{x \rightarrow 0^{-}} f(x)$ is equal to

If $P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a $3 \times 3$ matrix $A$ and $|A| = 4$,then $\alpha$ is equal to:

The part of the castor seed from which oil is obtained is called the .....

Vedclass Test Series

Exam Paper Generator

Online Exam Module