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.

	Color
Model	Blue	Brown	White
XK​-50	290	100	205
CD​-99	47	206	126

a. Based on the relative frequency assessment​ method, what is the probability that a manufactured item is

blue​?

​P(blue​)=nothing

​(Round to four decimal places as​ needed.)b. What is the probability that the product manufactured is

a

CD-99​?

​P(CD-99​)=nothing

​(Round to four decimal places as​ needed.)c. What is the probability that a product manufactured is

a

CD-99

and

blue​?

​P(CD-99

and

blue​)=nothing

​(Round to four decimal places as​ needed.)d. Suppose a product was chosen at random. Consider the following​ events: the event that model

CD-99

was chosen and the event that a

white

product was chosen. Are these two events mutually​ exclusive? Explain.

Answer 1

The table given to us is as follows. Modelo color Brown Blue white Total XK -50 290 100 205 595 CD-99 47 206 126 379 Total 337 306 331 1974 (a) We have to find the probability that manufactured item is blue That is, P(blue) Number of blue bikes PC blue) Total number of bikes 337 O. 345995 974 Ť 0.346 Thus, the probability that a manufactured item is blue 0.346 So the answer is PC blue ) - 0.346 (b) We have to find the probability that, the product manufactured is a CD-99. That is, we have to find PCCD-99)

P(CD-99) Number of CD-99 bikes Total number of bikes 379 974 0.3891 Thus the probability that a product manufactured is a CD-99 is 0.3891 So the answer is P(CD-99) = 0.3891 (C) We have to find the probability that the manufactured is a CD-99 and blue. That is, we have to find PCCD-99 and blue ) No. of bikes which are CD-99 and its colod is blue 4T Then PCCD-99 and blue ) = No. Of bikes which are CD-99) and blue Total number of bikes 4T 974 = 0.0483 Thus, the probability that a product manufactured is a CD-99 and blue is 0.0483 Thus the answer is P(CD-99 and blue )= 0.0483

(d) Let 4 be the event, a product was chosen at random was CD-99 model Let B be the event that a klhite product was chosen We have check whether these two events are mutually exclusive Mutually exclusive events – they cannot Occur together That is two events A and B should be disjoint → PCAB)0 Here PC40B) = PC CD99 and White ) =P ( Product chosen was CD-99 and white) =(number of products which are CD-99 and white) Total numbey of bikes. 126 974 0.1294 Here AOB is not disjoint, Because there is 126 bikes which are CD-99 and White in color. Also P(40B) - 0.1294 to

Here, PC AUB) = P(AOYB) = P(A) + P(B) - P(AB) P(CD-99) + P( White ) - P(CD-99&white) 0.3891 + 0.3398 -0.1294 0.5995 Here PCAUB) + PCA)+ P(B) A and B are mutually exclusive if P (AUB) - P (4) + PCB) Here PCAUB) # PCA) + PCB) → A and B are not mutually exclusive Thus, the two events exclusive qve not mutually So the answer is events are not mutually exclusive