00:01
Of all the registered automobiles in a city, 12 % fail the emissions test.
00:09
14 automobiles are selected at random to undergo an emissions test, round the answers to four decimal places.
00:17
So first we're going to find the probability that exactly three of them fail.
00:22
And this is a binomial distribution, so we can do 14 combination 3 times 0 .12 to the third power, times 1 minus 0 .12, which is 0 .88 to the 11th.
00:35
And that's going to give us 0 .1542.
00:40
Part b, find the probability that fewer than three, so x is less than three is what we're finding.
00:50
And we can find that by finding the probability of 0 and adding it to the probability 1 and adding it to the probability of 2.
00:58
So the probability of 0 is 14 combination 0 times 0 .12 to the 0 power times 0 .88 to the 14th power.
01:07
And that is 0 .1670, probability of 1 is 14, combination 1 times 0 .12 to the first power times 0 .88 to the 13th power, and that is 0 .3188, and the probability of 2 is 14, combination 2 times 0 .12 squared, times 0 .88 to the 12th power...