CT4 2009 April 8

[Priyanka Malhotra]

Hi could someone please help me understand that expression from examiner report: "So the probability of a meeting resulting in an increase in the number of cats with fleas is 0.5x(10 − x)/45.." in part ii examiner's report has 0.5 in numerator because "Whenever a cat which has fleas meets a cat without fleas, there is a 50% probability that some of the fleas transfer to the other cat such that both cats harbour fleas thereafter." is given in the question?
Then where should we adjust "meetings are equally likely to involve any of the possible pairs of individuals" given in the question.. thanks in advance!

 

[Busy_Bee4422]

Hi
The part x(10-x)/45 is the one adjusting for the pairings that increase cats with fleas. The x(10-x) tells you the number of pairings that may result in an increase from part i and the total number of pairings is 45 so the fraction of pairings with possible increase is x(10-x)/45. But only 50% of these result in an increase so we multiply by the 0.5 to get 0.5x(10-x)/45.

 

[Priyanka Malhotra]

Hi, thank you so much for explaining this! I am still confused however that where would we adjust "meetings are equally likely to involve any of the possible pairs of individuals" given in the question

 

[Busy_Bee4422]

Hi
The 45 is the one that is counting all meetings. If they are all equally likely then the probability of each meeting is simply 1/45. Since there are x(10-x) meetings that increase the number of fleas you get the probability of meetings increasing fleas to be x(10-x)/45.