In a video game, gate 3 is open 40% of the time and gate 4 is open 20% of the time. the chance of both gates being open at the same time is 15%. draw a tree and venn diagram (with probabilities labeled) to model the scenario. what is the p(gate 3 and gate 4 are both open)? a.60% b.15% c.100% d.0%

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?