statisics questions

Question

1) A basketball player makes 70% of his free throws. We put him on the free-throw line and ask him to shoot free-throws until she misses. Let X= the numer of free throws the player takes until he misses.
a) what is p? (be careful. we are looking for the # of free throws until she misses)
b) assuming that his shots are independent, what is the probability that he will make 5 shots before she misses
c)what is the probability that he misses his first free throw?
show work please
2) the probability that an individual has 20-20 vision is .20. in a class of 36 students what is the probability of finding exactly 6 people with 20-20 vision.(show work)
3) the university kpolice department must write, on average, eight tickets per day to keep department revenues at budgeted levels. suppose the numer of tickets written per day follows a poison ditribution with a mean of 10 tickets per day. find the probability that less than eight tickets are written on a randomly selected day from his distribution
4) a history professor finds that when he schedules an office hour at the 1030 am time slot an average of four students arrive. use the poison distribution to find the probability that in a randomly slelected office hour in the 1030 am time slot exactly five students will arrive.
5)the probability that a football game will go into overtime is 13%. what is the probability that two of five football games will go into overtime

Answer 1

1)

b) probability 5 throws before she misses= .7^5(.3) = about .05 = 5% chance

c) 100-70 = 30% chance of missing on 1st throw