Azoo train ride costs $2 per adult and $1 per child. on a certain day, the total number of adults (a) and children (c) who took the ride was 33, and the total money collected was $44. what was the number of children and the number of adults who took the train ride that day, and which pair of equations can be solved to find the numbers?

11 children and 22 adults
equation 1: a + c = 33
equation 2: 2a – c = 44
11 children and 22 adults
equation 1: a + c = 33
equation 2: 2a + c = 44
22 children and 11 adults
equation 1: a + c = 33
equation 2: 2a – c = 44
22 children and 11 adults
equation 1: a + c = 33
equation 2: 2a + c = 44

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?