Anita has a success rate of 80% on free throws in basketball. She wants to know the estimated probability that she can make exactly four of five free throws in her next game. How can she simulate this scenario? Categorize each simulation of this scenario as correct or incorrect.

Roll a six-sided die five times. The
numbers 1 to 4 represent a make,
and numbers 5 and 6 represent a
miss.
Spin a spinner with three equal
sections five times. On the spinner,
one section represents a miss and
two sections represent a make.
Generate a set of five numbers using
a number generator with the numbers
0 to 9.The numbers 0 to 7 represent a
make, and 8 and 9 represent a miss.
Generate a set of five numbers using
a number generator with the numbers
0 to 5.The numbers 0 to 3 represent a
make, and 4 and 5 represent a miss.
Spin a spinner with five equal sections
five times. On the spinner, four sections
represent a make and one section
represents a miss.

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?