Extreme math problem. PRE CALC?

[Jack Black]

Can you help me solve a math problem for my final exam? It is on the review

Rick was recently diagnosed with a chance of having HIV after engaging in deviant activity with multiple partners. If Rick had a total of three sex partners before his diagnosis, calculate the chance that one of his partners transmitted him HIV.

One of his partner's Luke has a 35% chance of having HIV. Rick engaged in butsex a total of 3 times with Luke.
Rick had sex with a priest known as Charlie. Charlie had a 60% of transmitting HIV, and Rick had intercourse a total of 2 times with Charlie.
Rick's husband, Matt, had but sex with Rick a total of 5 times. Matt has a 25% chance of transmitting HIV on each occasion.

Calculate the chance of getting HIV from each partner. Write a piecewise function g(a) that describes the probability of transmitting HIV from each of his partners.
yah my teacher is an ignorant asshole. i go to a private catholic school so he is homophobe

[Vera Keys]

it is english -.- learn it some time and its a calculator paper =/ if i can remember ._. .. anyway sorry =/ i dont know that its a little too complicated for me im afraid

[Tsubaki]

EDIT: Fixed errors on the piecewise.

From Luke:
p(getting HIV) = 1 - p(not getting HIV)
= 1 - (1 - 0.35)^3
= 0.725375 or 72.5%

From Charlie:
= 1 - (1 - 0.6)^2
= 0.84 or 84%

From Matt:
= 1 - (1 - 0.25)^5
= 0.762695 or 76.3%


For the piecewise function, first assume that the problem asks for probability of contracting HIV as a function of the number of sexual encounters, and that these encounters are chronologically ordered as written in the problem. Then just use the same formula and add them together:
g(a) =
1 - (0.65)^a when 1<=a<=3
2 - (0.65)^3 - (0.4)^(a-3) when 4<=a<=5
3 - (0.65)^3 - (0.4)^2 - (0.75)^(a-5) when 6<=a<=10

And if you're interested, the chance that Rick gets HIV after he has had all the sex is
1 - p(not getting HIV from any of them)
= 1 - (1-0.725375)(1-0.84)(1-0.762695)
= 1 - 0.010427
= 0.989573 or 98.96%

So Rick is pretty much guaranteed to contract HIV and die a terrible death.
Your teacher has a peculiar sense of humor. :/