Question

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

Find the probability that, in one day:

i) A sells two iPods [2 Marks]

ii) A sells just one iPod [2 Marks]

iii) B makes at least one sale [3 Marks]

iv) Between them A and B make exactly one sale. [4Marks]

Answer 1

i)

$$P(AA)=0.4(0.4)=0.16$$

ii)

$$P(A\ only\ 1)=P(AA^C)+P(A^CA)$$

$$=0.4(1-0.4)+(1-0.4)(0.4)=0.48$$

iii)

$$P(B\ at\ least\ 1)=1-P(B^CB^C)$$

$$=1-(1-0.1)(1-0.1)=0.19$$

iv)

$$P(only\ 1)=P(A\ only\ 1)P(B^CB^C)$$

$$+P(B\ only\ 1)P(A^CA^C)$$

$$=(P(AA^C)+P(A^CA))P(B^CB^C)$$

$$+(P(BB^C)+P(B^CB))P(A^CA^C)$$

$$=(0.4(1-0.4)+(1-0.4)(0.4))(1-0.1)(1-0.1)$$

$$+(0.1(1-0.1)+(1-0.1)(0.1))(1-0.4)(1-0.4)$$

$$=0.4536$$