A canal system is shown in the figure. Water flows from A to B through two channels. Gates $G_1$ and $G_2$ are operated independently to regulate the flow. Probability of $G_1$ to be open is 10% while that of $G_2$ is 20%. The probability that water will flow from A to B is
To calculate the probability of water flowing from A to B, we need to consider the scenarios in which the gates $G_1$ and $G_2$ are open because water can only flow if at least one gate is open.
Given:
- Probability of $G_1$ being open, \(P(G_1) = 0.10\)
- Probability of $G_2$ being open, \(P(G_2) = 0.20\)
The probability that both gates are closed is calculated as follows:
- Probability that $G_1$ is closed = \(1 - P(G_1) = 0.90\)
- Probability that $G_2$ is closed = \(1 - P(G_2) = 0.80\)
Therefore, the probability that both gates are closed is the product of both individual probabilities:
\(P(\text{Both Closed}) = 0.90 \times 0.80 = 0.72\)
Thus, the probability that at least one gate is open, allowing water to flow, is:
\(P(\text{At least one open}) = 1 - P(\text{Both Closed}) = 1 - 0.72 = 0.28\)
So, the probability that water will flow from A to B is 28%.
Therefore, the correct answer is 28%.
Important Questions from Probability (Notes)
- A box contains 20 black, 22 white, and 24 red socks. If a person draws socks at random one by one without looking, what is the minimum number of socks she must pick to be certain of having at least one pair of black socks?
The following bus schedule is seen at a bus stop located somewhere in between town A and town B.
Town A-00:10, then every 20 mins
Town B-00:15, then every 20 mins
If a person arrives at this bus stop at some random time, the probability that the next bus is for town B is- Some, but not all, faces of a six-faced cubical fair die are painted red (R) and the remaining green (G); and the die is thrown until red faces come up on top 4 times.
Consider the following sequences of colours listed left to right as they appear on the top.
A: GRRRR
B: GRGRRR
Which one of the following is true? - In a class, 40% and 20% students passed in Mathematics and Physics, respectively, and 10% students passed in both subjects. What is the probability of a randomly selected student to have passed in Physics if the student already passed in Mathematics?
- A stick of length L is broken into two pieces at random. What is the average length of the smaller piece?
