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)
- 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?
- Two students are solving the same problem independently. If the probability that the first one solves the problem is $\frac{3}{5}$ and the probability that the second solves the problem is $\frac{4}{5}$, what is the probability that at least one of them solves the problem?
- A fair die was thrown three times and the outcome was repeatedly six. If the die is thrown again what is the probability of getting six?
- 12 balls, 3 each of the colours red, green, blue and yellow are put in a box and mixed. If 3 balls are picked at random, without replacement, the probability that all 3 balls are of the same colour is
