Some math questions.

Factual Questions
1

If a, b, and c are positive integers such that a + 1/(b + (1/c)) = 37/16, what is a + b + c?

Two people got married. The probabilities that the man and the woman will live 45 more years are 0.58 and 0.64, respectively. Find the probability that both will still be alive 45 years later.

If 20% of the bolts produced by a machine are defective, determine the probability that out of 4 bolts chosen at random, less than two bolts will be defective.

I’m stuck on these particular items in my reviewer. :smack: Can somebody please explain how to solve these? Thanks. :slight_smile:

2

If a + 1/(b + (1/c)) = 37/16

Case 1: a = 1
1/(b + (1/c)) = 21/16
b + (1/c) = 16/21 – Impossible

Case 2: a = 2
1/(b + (1/c)) = 5/16
b + (1/c) = 16/5
Therefore b =3 and c=5

3

If the probabilities are independent, then the probability that both will still be alive is 0.58 times 0.64.

4

The probability that zero are defective: 0.80.80.80.8 = 0.4096
The probability that one is defective: 40.20.80.8*0.8 = 0.4096

So the answer is 0.4096 + 0.4096 = 0.8192

5

Just to add to the first answer that he essentially found the continued fraction expansion of 37/16, which is unique (if you require it be finite).

6

And if they’re not independent (which they may well not be in a real-world situation), there’s not enough information to answer the question.

This type of problem, where you’re interested in the probability of x defectives out of n bolts, is an example of the Binomial Distribution, which should be covered in any basic probability/statistics book.

7

thanks guys. this helped.