Consider the circuit shown in the image. If t | vedclass

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

Question

(NONE) The circuit consists of two parallel branches connected between points $A$ and $B$.$1$. The upper branch contains two switches $a$ and $b$ in s

Vedclass · Accepted Answer

$p^2 + p$

Vedclass · Answer

(NONE) The circuit consists of two parallel branches connected between points $A$ and $B$.$1$. The upper branch contains two switches $a$ and $b$ in series. Current flows through this branch only if both switches $a$ and $b$ are closed.Since the probability of each switch being closed is $p$,the probability that the upper branch is closed is $P(	ext{upper}) = p \cdot p = p^2$.$2$. The lower branch contains a single switch $c$. Current flows through this branch if switch $c$ is closed.The probability that the lower branch is closed is $P(	ext{lower}) = p$.$3$. Current flows from $A$ to $B$ if either the upper branch is closed $OR$ the lower branch is closed. Using the inclusion-exclusion principle for probability: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Here,$P(	ext{upper} \cup 	ext{lower}) = P(	ext{upper}) + P(	ext{lower}) - P(	ext{upper} \cap 	ext{lower})$.$P(	ext{upper} \cap 	ext{lower}) = p^2 \cdot p = p^3$.Therefore,the required probability is $p^2 + p - p^3$.

Consider the circuit shown in the image. If the probability that each switch is closed is $p$,then find the probability of current flowing through $AB$.

Similar Questions

$A$ coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows $6$ is

$A$ bag contains $7$ black and $5$ white balls. $A$ ball is drawn out and replaced in the bag. Then a ball is drawn again. What is the probability that the first ball was black and the second white?

$A$ and $B$ toss a coin alternatively,the first to show a head being the winner. If $A$ starts the game,the chance of his winning is

The probability that a man will be alive $25$ years hence is $0.3$ and the probability that his wife will be alive $25$ years hence is $0.4$. Find the probability that $25$ years hence,only the man will be alive.

$A$ bag contains $3$ red and $7$ black balls. Two balls are taken out at random,without replacement. If the first ball is red,what is the probability that the second ball is also red?

Vedclass Test Series

Exam Paper Generator

Online Exam Module