Question

You work at Best Buy’s Warehouse and just received a shipment of the latest iPhone 11s. However, due to the new supplier (the old supplier closed due to COVID-19), there are 4 defective phones in the shipment (but you don’t know which specific ones). Suppose there are 24 iPhones in the shipment. 

(a) (3 points) If three phones are randomly selected, find the probability that the first two phones are NOT defective but the last phone selected IS defective. 

(b) (4 points) If three phones are randomly selected, compute the probability that at least one phone selected is NOT defective. Is this unusual? Explain.

Answer 1

Total number of iphones = 24

Non defective phone = 24 - 4 = 20

defective phones = 4

(a) If three phones are randomly selected, find the probability that the first two phones are NOT defective but the last phone selected IS defective.

P[ first two phones are NOT defective but the last phone selected IS defective ] = P[ 1 non defective out of 24 ]*P[ 1 non defective out of 23 once 1 non defective is out ]*P[ 1 defective out of 4 once two phones are out ]

P[ 1 non defective out of 24 ] = 20/24

P[ 1 non defective out of 23 once 1 non defective is out ] = 19/23

P[ 1 defective out of 4 once two phones are out ] = 4/22

P[ first two phones are NOT defective but the last phone selected IS defective ] = (20/24)*(19/23)*(4/22)

P[ first two phones are NOT defective but the last phone selected IS defective ] = 1520/12144

P[ first two phones are NOT defective but the last phone selected IS defective ] = 0.1252

(b) If three phones are randomly selected, compute the probability that at least one phone selected is NOT defective. Is this unusual?

P[ at least one phone selected is NOT defective ] = 1 - P[ no selected is NOT defective ]

P[ no selected is NOT defective ] =

P[ no selected is NOT defective ] =

P[ no selected is NOT defective ] = 0.5632

P[ at least one phone selected is NOT defective ] = 1 - 0.5632

P[ at least one phone selected is NOT defective ] = 0.4368