Question

A bicycle company makes two mountain bike models that each come in three colors. Use the following table, which shows the production volumes for one week, to answer parts a through d. Model XK-50 FL-99 Color Blue Brown 290 90 38 207 White 191 127 a. Based on the relative frequency assessment method, what is the probability that a manufactured item is brown? P(brown) = (Round to four decimal places as needed.) b. What is the probability that the product manufactured is an XK-50? P(XK-50)=(Round to four decimal places as needed.) c. What is the probability that a product manufactured is an XK-50 and brown? P(XK-50 and brown)(Round to four decimal places as needed.) d. Suppose a product was chosen at random. Consider the following events: the event that model XK-50 was chosen and the event that a blue product was chosen. Are these two events mutually exclusive? Explain. O A. The two events are not mutually exclusive because the probability of the events occurring together is 0. O B. The two events are mutually exclusive because the probability of the events occurring together is 0. O C. The two events are mutually exclusive because the probability of the events occurring together is not 0 OD. The two events are not mutually exclusive because the probability of the events occurring together is not 0.

Answer 1

a.

P(brown) = brown bikes/total bikes

= (90 +207)/943

= 0.3149

b.

P(XK-50) = XK-50 bikes/ total bikes

= (290 + 90+ 191)/943

= 0.6055

c.

P(XK-50 and brown) = XK-50 and brown bikes/ total bikes

= 90/943

= 0.0954

d.

D. The two events are not mutually exclusive because the probability of the events occuring together is not 0