Question

Jeremy sells a magazine which is produced in order to raise money for homeless people. The probability of making a sale is 0.1 for each person he approaches. Given that he approaches 20 people, find the probability that he will make: a. 2 or fewer sales b. exactly 4 sales c. more than 5 sales

Answer 1

Solution: Given that p = 0.1, n = 20

Binomial distribution : P(X = r) = nCr*p^r*q^(n-r)

a. P(X <= 2) = P(0)+P(1)+P(2)
         
    = 0.1216+0.2702+0.2852
        
      = 0.6770

P(0) = 20C0*0.1^0*0.9^20 = 0.1216

P(1) = 20C1*0.1^1^0.9^19 = 0.2702

P(2) = 20C2*0.1^2*0.9^18 = 0.2852

b. P(X = 4) = 20C4*0.1^4*0.9^16 = 0.0898

c. P(X > 5) = 0.011
2  
   P(X > 5) = 1 - P(X <= 5)

       
          = 1 - (P(0)+P(1)+P(2)+P(3)+P(4)+P(5))
= 1 - (0.1216+0.2702+0.2852+0.1901+0.0898+0.0319)
= 0.0112