Suppose that a computer chip company has just shipped 5,000 computer chips to a computer company. Unfortunately, 20 of the chips are defective. (a) Compute the probability that two randomly selected chips are defective using conditional probability. (b) The probability that the first randomly selected chip is defective is 20 = 0.004 = 0.4%. Compute the probability that two randomly selected chips are defective 5,000 under the assumption of independent events. (a) The probability is. (Round to eight decimal places as needed.)

Suppose your top drawer contains 44 different colored socks: 6 are white,16 are black,10 are pink, and12 are blue. All socks in the drawer are loose (unpaired). In the morning, you randomly select two socks, one at a time. Calculate the following probabilities, writing your answer either as a decimal or a fraction.(a) What is the probability that you get a blue pair of socks?  (b) What is the probability that you do not get a blue pair of socks?   (c) What is the probability that neither is blue?  (d) What is the probability that you get either a white pair or a blue pair of socks?  (e) What is the probability that you get one black sock and one white sock?

Airline A is on time 80% of the time, Airline B is on time 85% of the time, and Airline C is on time 90% of the time. Airline A has twice as many flights as Airline B, and Airline B has three times as many flights as Airline C. One flight is selected at random from one of these airlines. (a)  What is the probability this flight on time? (b) Given that the flight is on time, what is the probability it is from Airline A?

One student is selected at random from a group of 200 known to consist of 140 full-time (80 female and 60 male) student and 60 part-time (40 female and 20 male) students.   Event A is "the student selected is full-time" and event C is "the student selected is female".   (a) Are events A and C independent?   (b) Find the probability of one student selected is full-time, that should be female.