The independent probabilities that three components of Television set will need replacement in a year , 1/10,1/12, and 1/15. Calculate the probability that one and only one component will needreplce ?

To calculate the probability that one and only one component will need replacement, we need to consider the probabilities of each component needing replacement individually and then multiply them together.

The probability that the first component needs replacement is 1/10.
The probability that the second component needs replacement is 1/12.
The probability that the third component needs replacement is 1/15.

To calculate the probability that one and only one component needs replacement, we need to consider three scenarios:
1. The first component needs replacement, but the second and third components do not.
2. The second component needs replacement, but the first and third components do not.
3. The third component needs replacement, but the first and second components do not.

For scenario 1:
Probability = (1/10) * (11/12) * (14/15) = 154/1800

For scenario 2:
Probability = (9/10) * (1/12) * (14/15) = 126/1800

For scenario 3:
Probability = (9/10) * (11/12) * (1/15) = 99/1800

Adding up the probabilities for each scenario:
Probability = (154/1800) + (126/1800) + (99/1800) = 379/1800

Simplifying the fraction:
Probability = 0.2106

Therefore, the probability that one and only one component will need replacement is approximately 0.2106.

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