Lightbulbs i. a room has three lightbulbs. each one has a 10% probability of burning out within the month. the next exercise refers to this. what is the probability that at the end of the month at least one of the bulbs will be lit? write the probability as a percentage. (fill in the blank below and round your answer to 1 decimal place.) the probability that at the end of the month at least one of the bulbs will be lit is 0.1 %.

The probability that at least one will be lit is 99.9%.

To find the probability that at least one is lit we start with the probability that they all burn out:

(0.1)(0.1)(0.1) = 0.001

The probability that one or more of them is lit is 1-(the probability none are lit):
1 - 0.001 = 0.999 = 99.9%

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AFOKE88 AFOKE88 · Answer 2 · 2021-10-01T18:52:13+02:00

This is about permutations and Combinations.

Probability of at least one of the bulb being lit by month end = 99.9%

We are told that there are 3 lightbulbs in the room.

Each bulb has a probability of burning out within the month at 10%.

Thus; P(burn out within a month) = 10% = 0.1

Thus; the probability that they will all burn out is;

P(All bulbs burn out) = 0.1 × 0.1 × 0.1 = 0.001

Now, the probability that at least one of the bulbs will be lit is;

P(at least 1 bulb to be lit) = 1 - P(All bulbs burn out)

P(at least 1 bulb to be lit) = 1 - 0.001

P(at least 1 bulb to be lit) = 0.999 or 99.9%

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