Question

7. Below is a diagram that shows water flowing from left to right. After branching into two smaller stream, the water must proceed through a series of dams which allow the water to pass (when functioning) and which stop water flow (when broken). Each dam is independent of the others and functions correctly with probability p. What is the probability San Diego will have water? AM DAM SAN DIEÇO DAM DAM water Source Hint: Let T be the event that water successfully makes it through the top path. Let B be the event that water successfully makes it through the bottom path. Simplify your answer as much as possible. (You should check your final answer makes sense by plugging in p-0 and also p-1. In those cases, you should know for sure what will happen in San Diego!)

Answer 1

This is a case of Bernoulli Distribution which is a random experiment in which there are only two outcomes namely SUCCESS and FAILURE.

In this question as well, either the dams allows the water to pass or stops the water flow.

BERNOULLI DISTRIBUYION:

P(X0otherwise

Let T be the event that water successfully makes it through the top path then

P(T-t)-Plor" otherwise

Let B be the event that water successfully makes it through the bottom path then

P(Botheruise

We need to find the probability of san diego having water.

We know San diego will have water either through the top path or through the bottom path

P(S) = probability that san diego will have water

P(S) = P(T=t) + P(B=b) as both the events are independent of each other.

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