Statistics question regarding chance.?

Question

My boss says his wife got pregnant while on the pill and his excuse was since the pill has an effectiveness of 99.997% each time, after having sex 1000 times, there should be 3 times where it wont work. Is this a correct interpretation of those statistics?

Answer 1

p = prob of not getting pregnant
= 1 - 0.99997 = 3 x 10^-5

n = 1000
So expected no. of pregnancies = np
= 3 x 10^-2 = 0.03

They need to have sex 100,000 times to have an expectation of 3 pregnancies. Tell him to divide his percentages by 100. And tell her to remember to take her pills.

Answer 2

ON AVERAGE, the pill will not work three times out of ten thousand with the population with which it was tested. There is no assurance that the boss has a wife belonging to the tested population (she may be more or less likely than the average person to become pregnant). In any event, and most importantly, statistics are rarely of much help at extreme values of distribution ranges.

Answer 3

in the simplest of terms, yes. percentages are nothing but a chance of something happening. the can be written as ratios, odds, percentages, and several other ways but if we turn 99% into and odd that means that 99 out of 100 times something will or wont happen. so with your information, 99997 times they should not get pregnant, but 3 times they may out of 100000 times.
Of course these are statisitcs and under the ideal sitations. Even taking the pill two hours latter than the normal routine time, alters the body slightly and may increase chances of pregnancy. It is also known that antibiotics decrease the effectivness if the pill.
In short. For the most part you are right, but there are many other factors at play for this specific case.

Answer 4

No, and it's not good arithmetic, either.