1. An exam has a pass rate of 0.62. The probability that someone who passed answered an item correctly is 0.87. Those that failed answered the item correctly 0.13 proportion of the time. What is the probability of passing given that a test taker got the item correct?
2. The probability an item is answered correctly is 0.77. Those that pass answer the item correctly 0.96 proportion of the time. Those that answer correctly pass 0.76 proportion of the time. What is the pass rate of those who answer this item incorrectly?