Let P ( A ) = 0.5, P ( A ∩ B ) = 0.2 and...

Let P ( A ) = 0.5, P ( A ∩ B ) = 0.2 and P ( A | B ) = 0.5. Determine P ( B ) = (as a decimal) and P ( A ∪ B ) = (as a decimal)
Three identical light bulbs are connect in parallel. If the probability of the system to operate normally is 99.2%, determine the probability of each light bulb to fail p = (as a decimal).

Solutions

Expert Solution

1. There are two events A and B. We are given the probabilities:

The conditional probability is given using the formula:

Substituting the values in the formula, we get:

Next, we are to determine the probability:

This can be calculated using the formula:

Substituting the values in the formula, we get:

2. Three identical bulbs are arranged in parallel. Let the probability of either of them failing be p and the probability of each of them working be q and q = 1 - p.

Now, the system will operate when either of the bulbs glow. Let the three bulbs be A, B and C. Hence, the probability that the system will not operate is:

The probability of this will be:

Now we have the probability of either of them failing is:

Hence, the probability of each of them failing is:

Thus, we have:

Hence, the probability of each of the light bulbs to fail is p = 0.4309

orchestra answered 1 year ago

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