Thanks for the very good Question Mike.
But I got 2044/3125. I just tried , But i will wait for your answer
Theresa to make basket atleast 4 times= [Theresa Making the basket for 4 times + Theresa making the basket for 5 Times]Theresa Making the basket for 4 times :- [Let Y be hit and M be Miss]
C ase 1 :- YYYYM(Miss in the 5th throw)Probability of First time hit is always 0.6 = 3/5
3/5*4/5*4/5*4/5*4/5
= 368/3125
Case 2 :- YYYMY(Miss in the 4th throw)Probability of First time hit is always 0.6 = 3/5
3/5*4/5*4/5*4/5*2/5
the 2/5 because 4th one is Miss
= 384/3125
Case 3 :- YYMYY(Miss in the 3rd throw)Probability of First time hit is always 0.6 = 3/5
3/5*4/5*4/5*2/5*4/5
(this 2/5 because 3rd one is Miss)
= 384/3125
Case 4 :- YMYYY(Miss in the 2nd throw)Probability of First time hit is always 0.6 = 3/5
3/5*4/5*2/5*4/5*4/5
(this 2/5 i because 2nd one is Miss)
= 384/3125
Case 5 :- MYYYY(Miss in the 1st throw)Probability of First time hit is always 0.6 = 3/5
hence the probability of first time miss is (1-3/5) =2/5
2/5*2/5*4/5*4/5*4/5
(this 2/5 in the second position because 1st one is Miss)
= 256/3125
Probability(Theresa Making the basket 4 times) = 368/3125 + 384/3125+384/3125+384/3125 + 256/3125
= 1676/3125
Theresa making the basket for 5 Times :-only one case
case 1 :- YYYYYProbability of First time hit is always 0.6 = 3/5
3/5*4/5*4/5*4/5*4/5
Probability(Theresa Making the basket 5 times) = 368/3125
Probability(Theresa Making the basket atleast 4 times) = Probability(Theresa Making the basket 4 times) + Probability(Theresa Making the basket 5 times)
= 1676/3125 + 368/3125
= 2044/3125
3125(5 to the Power 5)
Awaiting for your correct Answer!!!