a. AG electronics, purchases TV picture tubes from four different suppliers. Ami

Question

a. AG electronics, purchases TV picture tubes from four different suppliers. Amit Wholesale supplies 20 percent of the tubes, Bob Importers 30 percent. Cooks 25 percent and Danni 25 percent. Amit Wholesale tends to have the best quality of product, as only 3 percent of its tubes arrive defective. Bob Importers tubes are 4 percent defective. Cooks 7 percent defective and Danni 6.5 percent defective. In the assembly line of AG electronics, one of the picture tube found to be defective. i. What is the probability that it was from Amit Wholesale? ii. What is the probability that it was from Danni? b. TABLE Q2 illustrates the coffee consumption habit in Perak state. A survey of 300 respondents revealed that the following. TABLE Q2: Coffee consumption habit Construct a tree diagram showing all the marginal probabilities, conditional probabilities and joint probabilities.

Explanation / Answer

Ans:

2a)Probability of a defective=0.03*0.2+0.04*0.3+0.07*0.25+0.065*0.25=0.052

i)Probability that it was from Amit wholesale=0.03*0.2/0.052=0.115

ii)Probability that it was from Danni=0.065*0.25/0.052=0.3125

b)

Marginal probabilites:

P(low)=0.3,P(moderate)=0.333,P(high)=0.367

P(under 30)=0.307,P(30-40)=0.250,P(40-50)=0.180,P(above 50)=0.263

Conditional probabilities:

P(low/under 30)=P(low and under 30)/P(under 30)=0.120/0.307=0.391

similarly,

Low moderate high Total under 30 36 24 32 92 30-40 18 27 30 75 40-50 10 20 24 54 above 50 26 29 24 79 Total 90 100 110 300 Joint probability distribution: Low moderate high Marginal under 30 0.120 0.080 0.107 0.307 30-40 0.060 0.090 0.100 0.250 40-50 0.033 0.067 0.080 0.180 above 50 0.087 0.097 0.080 0.263 Marginal 0.300 0.333 0.367 1

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