Sorry for the constant posts but this one is doing my head in. I can't find the answer to the 2nd part of e) a more direct way of finding the probability of being chosen for one of the parts
these are my answers so far:
a) 7P2 = 42
b) since the other position is filled there are 6 ways to fill the part for the heroine - so 6
e) let A = being chosen for the heroine
B = being chosen for the best friend
then P(A u B) = 6/42 + 6/42 = 2/7
but what is the direct route for finding this probability? I thought perhaps I could use the rule 1 minus the complement of being being chosen...but then I dont know how to calculate the probability of not being chosen!!!
I think I've got it!
the probability of not being chosen is found by finding the number of ways in which the 6 remaining people can be ordered (6P2 = 30) divided by the total number of ordering of the 7 people (7!)
so let A be the probability of being chosen for one of the 2 roles
then P(A) = 1-P(Ac) = 1-(30/42) = .28571
which is equal to 2/7
thats the right way of doing it....right?