Question

A firm buys 3 shipments of parts each month. The purchasing agent selects at random from among four in-state suppliers and six out-of-state suppliers. What is the probability that orders are placed with
a) The in-state suppliers only
b) The out-of-state suppliers only
c) At least one in- state suppliers

Answer 1

Let the purchase from an in-state supplier be denoted by X

Let the purchase form an out-state supplier be denoted by Y

The following tree diagram shows all the possible probabilities

a) P(In-state supplies only) = P(XXX)

$=\frac{4}{10}*\frac{3}{9}*\frac{2}{8}=0.0333$

b) P(Out-state suppliers only) = P(YYY)

$=\frac{6}{10}*\frac{5}{9}*\frac{4}{8}=0.1667$

c) P(At least one in-state supplier) = 1 - P(out-state suppliers only)

$=1-0.1667 = 0.8333$