Question

Christmas Tree lights are used not only for Christmas trees, but sometimes to decorate college dorm rooms. Suppose that a string has 20 light bulbs. These lights are all wired in series, so that if one light bulb fails, the whole string fails. The probability that any one light fails is 0.02. Each of the individual lights are independent of each other. What is the probability that the string will NOT fail?
a. 0.02
b. 0.40
c. 0.668
d. 0.333

Answer 1

Answer: Hello!

Ok, because the bulbs are wired in series, then if only one fails, all the string fails.

Then we need to see the probability for the 20 bulbs to not fail.

If the probability for each bulb to fail is 0.02, then the complement (or the probability of working fine) is 1 - 0.02 = 0.98

then we have 20 bulbs, and each one has a probability of 0.98 of working alright, then the probability for all them to work alright is the multiplication of this probabilities, this is

$0.98^{20}$ = 0.6676

rounded up in the decimal, we have 0.668

then the correct answer is c.