Math help?

[Marilyn431]

The prince has searched all over his kingdom for the maiden who left the glass slipper at the ball. He will not recognize her by sight, but will use the abandoned slipper to determine who the maiden is. He arrives at the house where Cinderella and her three step-sisters live. The prince tries the slipper on one of the four sisters at random. If it does not fit, he will pick another sister to try it on, and so on, until he finds Cinderella. What is the expected number of times he must try the slipper (in this house)?

and

When all factors are taken into account, an insurance company estimates that the probability of the owners of a certain house making a claim for $7,000 is 0.18, and the probability of the house and contents being totally destroyed is 0.005. Should that tragedy happen, the company will have to pay $187,000. The company charges $2,300 for the insurance policy. What is the expected value of this policy to the insurance company?

 

[tkhunny]

An excellent Survival Model.

Get it on the first try.
p(1) = 1/4
Miss the first and get it on the second.
p(2) = (3/4)*(1/3) = 1/4
etc.
p(3) = (3/4)*(2/3)*(1/2) = 1/4
p(4) = (3/4)*(2/3)*(1/2)*1 = 1/4

Well, that rather makes sense.

There's your distribution. Can you calculate the expected value?

 

[tkhunny]

When all factors are taken into account, an insurance company estimates that the probability of the owners of a certain house making a claim for $7,000 is 0.18, and the probability of the house and contents being totally destroyed is 0.005. Should that tragedy happen, the company will have to pay $187,000. The company charges $2,300 for the insurance policy. What is the expected value of this policy to the insurance company?

You have the entire distribution. What's holding you back? You collect the Premium and then think about it.

0.005*(2300-187000) + 0.18*(2300-7000) + (1-0.18-0.005)*(2300)

That's about it. Were you thinking it was trickier than that?