A distribution center tested 10 automated barcode scanners.

Question

A distribution center tested 10 automated barcode scanners. Each scanner repeatedly attempted to read the same type of damaged barcode. For each scanner, the probability of a correct reading was the same on every attempt, and the outcomes of the attempts were independent. The table shows the probability that each scanner will read the barcode correctly on a single attempt and the minimum required probability of obtaining at least one correct reading.

Scanner  
  Probability of correct reading
on one attempt  
  Required probability of
at least one correct reading  
 
  1 
 0.25 
 0.70 
 
  2 
 0.30 
 0.80 
 
  3 
 0.50 
 0.95 
 
  4 
 0.35 
 0.85 
 
  5 
 0.15 
 0.60 
 
  6 
 0.20 
 0.75 
 
  7 
 0.40 
 0.88 
 
  8 
 0.45 
 0.90 
 
  9 
 0.28 
 0.82 
 
  10 
 0.32 
 0.92

For each of the following scanners, select  At most 5 attempts  if the minimum number of attempts needed to achieve at least the required probability shown in the table is at most 5. Otherwise, select  More than 5 attempts .

Bunuel · Accepted Answer

Official Solution:

For n independent attempts, each with probability p of a correct reading, the probability of at least one correct reading is:

1 - (1 - p)^n

Since we only need to determine whether the minimum number of attempts is at most 5 or more than 5, we can simply check the probability after 5 attempts:

If 5 attempts achieve the required probability, the answer is  At most 5 attempts . 
 If 5 attempts do not achieve the required probability, the answer is  More than 5 attempts .  
 
• Scanner 2

For Scanner 2, the probability of a correct reading on one attempt is 0.30, and the required probability is 0.80.

With 5 attempts:

1 - 0.70^5 ≈ 0.832

Since 0.832 is greater than 0.80, 5 attempts are sufficient.

Answer:  At most 5 attempts .
 
• Scanner 6

For Scanner 6, the probability of a correct reading on one attempt is 0.20, and the required probability is 0.75.

With 5 attempts:

1 - 0.80^5 ≈ 0.672

Since 0.672 is less than 0.75, 5 attempts are not sufficient.

Answer:  More than 5 attempts .
 
• Scanner 8

For Scanner 8, the probability of a correct reading on one attempt is 0.45, and the required probability is 0.90.

With 5 attempts:

1 - 0.55^5 ≈ 0.950

Since 0.950 is greater than 0.90, 5 attempts are sufficient.

Answer:  At most 5 attempts .

LogicDriven · Answer

Scanner 2,At most 5 attempts
Scanner 6,More than 5 attempts
Scanner 8,At most 5 attempts

P(at least 1 success) = 1 - (1 - p)^n

officiisnobis · Answer

2 - At most 5 
6 - More than 5
8 - At most 5

A distribution center tested 10 automated barcode scanners.

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Scanner	Probability of correct reading on one attempt	Required probability of at least one correct reading
1	0.25	0.70
2	0.30	0.80
3	0.50	0.95
4	0.35	0.85
5	0.15	0.60
6	0.20	0.75
7	0.40	0.88
8	0.45	0.90
9	0.28	0.82
10	0.32	0.92

At most 5 attempts	More than 5 attempts
		Scanner 2
		Scanner 6
		Scanner 8

GMAT Graphs and Tables (G&T) Questions

A distribution center tested 10 automated barcode scanners.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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Perfect 805 Score Debrief by Julia

My Rewards