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)

$$=\frac{4}{10}\cdot\frac{3}{9}\cdot\frac{2}{8}=\frac{1}{30}=0.0333$$

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

$$=\frac{6}{10}\cdot\frac{5}{9}\cdot\frac{4}{8}=\frac{1}{6}=0.1667$$

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

$$=1-\frac{1}{6}=\frac{5}{6} = 0.8333$$