MathDB

A basketball player has a constant probability of

.4

of making any given shot, independent of previous shots. Let

a_{n}

be the ratio of shots made to shots attempted after

n

shots. The probability that

a_{10}=.4

and

a_{n}\le .4

for all

n

such that

1\le n \le 9

is given to be

p^{a}q^{b}r/(s^{c}),

where

p,

q,

r,

and

s

are primes, and

a,

b,

and

c

are positive integers. Find

(p+q+r+s)(a+b+c).

Problem Statement