Question

1- A sample of 2 different calculators is randomly selected from a group containing 13 that are defective and 8 that have no defects. Assume that the sample is taken with replacement. What is the probability that at least one of the calculators is defective? Express your answer as a percentage rounded to the nearest hundredth.

2- Use the data in the following​ table, which lists​ drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. ​

Drive-thru Restaurant  /  A  /  B  /  C  /  D
Order Accurate         / 27 / 35 / 21 / 19
Order Not Accurate     / 1 / 40 / 10 / 21

If one order is​ selected, find the probability of getting an order from Restaurant C given the order that is accurate. Express your answer as a percentage rounded to the nearest hundredth.

Answer 1

1.

Number of defective calculators in the group = 13

Number of calculators with no defects in the group =8

Total number of calculators in the group = 13+8 =21

A sample with replacement of 2 different calculators is randomly selected from the group.

Probability that at least one of the calculators is defective = 1 - Probability that both the calculators are with no defects.

Probability that both the calculators are with no defects

= Probability that first calculator is with no defects x Probability that second calculator is with no defects

Probability that first calculator is with no defects = Number of calculators with no defects / Total number of calculators = 8/21

As the sample is taken with replacement, first calculator is put back in the group.

Therefore, the group of calculators is intact(13 that are defective and 8 that have no defects)

Probability that second calculator is with no defects = Number of calculators with no defects / Total number of calculators = 8/21

Probability that both the calculators are with no defects = (8/21)x(8/21) =64/441

Probability that at least one of the calculators is defective

= 1 - Probability that both the calculators are with no defects.

= 1- 64/441 = 377/441 = 0.854875

Probability that at least one of the calculators is defective = 85.4875%

Probability that at least one of the calculators is defective = 85.49%

2 -

Drive-thru Restaurant	A	B	C	D	Total
Order Accurate	27	35	21	19	102
Order Not Accurate	1	40	10	21	72
Total	28	75	31	40	174

If one order is​ selected, Probability of getting an order from Restaurant C given the order that is accurate

= Number of accurate orders from Restaurant C / Total number of accurate orders

= 21/102 = 0.205882

If one order is​ selected, Probability of getting an order from Restaurant C given the order that is accurate = 20.5882%

If one order is​ selected, Probability of getting an order from Restaurant C given the order that is accurate = 20.59%