It is almost 5am and I have been working this problem going over all my materials again and again for hours and cannot seem to figure this question out! :mad:

A mortgage holding company has found that 2% of its mortgage holders default on their mortgage and lose the property. Furthermore, 90% of those who default are late on at least two monthly payments over the life of their mortgage as compared to 45% of those who do not default. What is the joint probability that a mortgagee has two or more late monthly payments and does not default on the mortgage?

This is the stuff I've tried so far, am I even on the right track? Do I use Baye's Theorm? If yes how do I break up the categories? I am SO confused, PLEASE HELP!

Event Frequency
Default 2
do not default 98
default and late 1.8
do not default & late 44.1

Of 100 people 2% (2) default, of those 2 people 90% (1.8) are late.
Of 100 people 98% (98) do no default, of those 98 people 45% (44.1) are late
.018+.441
P(AorB)= P(A)+P(B)- P(A and B)
P(AorB)= P(.4490)+P(.98)- P(.441)

I think you already have your answer. You have figured that of 100 people the expected number who do not default and are late is 44.1%. That's it.