Probability:

Question

involving the assignment of tasks to student union board members. Assume that there are 15 board members: 10 females, and 5 males including Tom. There are 2 tasks to be assigned randomly, including that of taking minutes of meetings. There is at most one task per person.
(1) Find the probability that Tom is given a task.


(2) Find the probability that Tom is given the task of taking minutes of meetings.

Answer 1

2 is the simpler question here.  There are 15 people who could be randomly given the task of whom Tom is one.  The probability that he's the one who gets it is then just 1/15.  It's fairly straightforward to see that order of assignment doesn't affect this.  Imagine that the other task is assigned first; if Tom is assigned to it (a 1 in 15 chance), then he has 0 chance of also being assigned to take minutes.  If he is not assigned to it (a 14 in 15 chance), then he has a 1 in 14 chance of being assigned to take minutes.  This would make his probability of being assigned to take minutes 14/15 * 1/14 = 1/15, exactly the same as if you ignored the other task entirely.

 

Part 1 can be naively calculated by observing that there are 2 tasks to be given, and 15 people, making Tom's chance of being given a task 2/15.  The more formal solution is to observe that he has a 1/15 chance of being given the first task, and as noted above, a (14/15)*(1/14) = 1/15 chance of being given the second task, making his total chance of being given a task 2/15.  You could also calculate his chances of NOT being given a task at all ( 14/15 * 13/14 = 13/15) and then take its inverse, which also gives 2/15.