Probability of success is P = 10% = 10/100 = 1/10
Probability of failure is q = 1 - p = 1 - 1/10 = 9/10
Probability that he required less than or equal to 50 calls to make 10 successful sales
is P(E \(\leq\) 50) = P(10) + P(11) + P(12) +.... P(50)
= 10C10(1/10)10 + 11C10(1/10)10 9/10 + 12C10(1/10)10(9/10)2+....+50C10(1/10)10(9/10)40
(\(\because\) Minimum 10 calls are required)
\(\therefore\) probability that he needs to make more than 50 calls in P(E > 50) = 1 - p(E \(\leq\) 50)
= 1 - ((1/10)10 + 11C10(1/10)10 9/10 + 12C10(1/10)10(9/10)2)+ ...+ 50C10(1/10)10(9/10)40
= 1 - (1/10)10(1 + 11C109/10 + 12C10(9/10)2+....+50C10(9/10)40)