Answer to Question #178482 in Statistics and Probability for Wesley

Question

a)   Two vacuum cleaner salesmen A and B must each make two calls per day, one in the morning and one in the afternoon. A has a probability 0.4 of selling a cleaner on any call, while B (a novice) has a probability 0.1 of a sale. A works independently of B and, for each salesman, morning and afternoon results are independent of each other.

Find the probability that, in one day:

    i.       A sells 2 cleaners

   i.       A sells just one cleaner

  ii.       B makes at least one sale

 iii.       Between them, A and B make exactly one sale

Answer 1

i)

P(2) = 2!/(2!(2-2)!) *0.4²*(1-0.4)^2-2 = 0.16

ii)

P(1) = 2!/(1!(2-1)!) *0.4¹*(1-0.4)^2-1 = 0.48

iii)

P(1) = 2!/(1!(2-1)!) *0.1¹*(1-0.1)^2-1 = 0.18

iv)

P(1) = P(A sells 1) and P(B sells 0) or P(A sells 0 and B sells 1)

= (0.48*0.82) + (0.36*0.18)

= 0.4582