1:

An iPhone is produced by five production lines and shipped to suppliers in 100-unit lots. Because testing requires destroying the phone, most suppliers test only a small number of phones before deciding to accept or reject a lot of incoming iphones. All five production lines produce at the same rate and typically produce 2% defective iPhones which are dispersed randomly among the produced iPhones. However, production line 1 suffered a mechanical difficulty and produced 5% defective iPhones during the month of April, but this only became known to the manufacturer after the iPhones were shipped. A supplier received a lot produced in April and tested three iPhones from this lot, of which one failed. What is the probability that the lot was produced on line 1? What is the probability that the lot came from one of the four other lines? Carefully draw a probability tree to show your answer including all branch probabilities (separately show how these were calculated).

2:

Approximately 1/125 of all births are fraternal twins and 1/300 of births are identical twins. Elvis Presley had a twin brother (who died at birth). What is the probability that Elvis was an identical twin? (You may approximate the probability of a boy or girl birth as 1/2.)

3: