The probability that all bulbs work is 0.99.
Calculating probability is broken down into several phases by the total probability rule, commonly referred to as the Law of Total Probability.
When you don't know enough about an event's probabilities to do so directly, you can utilize it to determine the likelihood of an occurrence, A.
Instead, you use a related event, B, to calculate the probability of A.
If the occurrence of one event has no bearing on the chance that the other will also occur, the two occurrences are said to be independent.
There are seven bulbs in all, and each one operates independently.
The probability of each bulb is 99.9% = 0.999
Let the probability of bulb working be 'p'
The probability that everything work = [tex]P^{7}[/tex]
The probability that everything will work= [tex](0.999)^{7}[/tex] = 0.993
Thus, the probability that all bulb will work is 99.3%.
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