SOLUTION: Suppose the string of Christmas lights you just bought has twenty-four bulbs wired in series. Suppose that each bulb has a 97% chance of “working” the first time current is a

Question 1152607: Suppose the string of Christmas lights you just bought has twenty-four bulbs
wired in series. Suppose that each bulb has a 97% chance of “working” the
first time current is applied. If at least one of the bulbs fails, then the
series will not work. What is the probability that the string of lights will
fail to work?

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

Let's first calculate the probability that the string of lights WILL work.
Then we'll subtract that from 1 to find the probability that it will FAIL
to work.

For the string of lights to WORK, that means:

the 1st bulb works AND the 2nd bulb works AND the 3rd bulb works AND ∙∙∙ the
24th bulb works.

So that's (0.97)(0.97)∙∙∙(0.97) to 24 factors or (0.97)²⁴ = 0.4814172219 
or a string will work about 48% of the time.  So the other 52% of the time a
string will fail. 

We calculate 1 - 0.4814172219 and get 0.5185827781 or a probability of
51.85827781% of the time that a string will fail, and then round that off
to as many decimal places as your teacher says to round it.

Edwin

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