Question

Assume you are starting to date someone. You are reasonably satisfied with the relationship and give it a value of 2. You can either have a big fight with probability .5 or a small fight with probability .5. If you have a big fight, there is a .8 probability of losing 2 points to your relationship status and a .2 probability of gaining 2 points. If you have a small fight, there is a probability of .6 of losing 1 point and gaining 1 point with probability .4. If your relationship ever has a value of negative or 0, you break off the relationship. If your relationship ever has a value of 5, then you ask the person to marry you. (Such a question either is answered with a yes and you live happily ever after or your relationship ends due to the added pressure of the question). Regardless the relationship either becomes permanent or ends after this question. What is the probability that your relationship will lead to a proposal? Also comment on the probability of this occurring if you were only marginally satisfied with the relationship (value of 1) and extremely satisfied (a value of 4). (Note, the threshold of 5 is just so you can solve the problem. I think real life should have a higher value.)

Please solve and show work clearly.

Answer 1

SOLUTION:

GIVEN THAT

   starting to date someone. You are reasonably satisfied with the relationship and give it a value of 2. You can either have a big fight with probability .5 or a small fight with probability .5. If you have a big fight, there is a .8 probability of losing 2 points to your relationship status and a .2 probability of gaining 2 points. If you have a small fight, there is a probability