You toss a dice 30 times and recorded the results in the table below. # on dice Results
1
3
2
8
3
7
4
5
5
3
6
4
1.) What is the theoretical probability that an even number will be rolled on a
number cube?
2.) What was the experimental probability of how many times an even number
was actually rolled using the table?
3.) Theoretically if you roll a number cube 36 times, how many times would you
expect to roll the number one?
4.) How many times did you actually roll the number one in the experiment?
My

F(n + 1) = f(n) – 8. if f(1) = 100, what is f(6)?

Ana earns 2.5% simple interest on $2,000 in her savings account. she does not make any deposits or withdrawals. after 3 years, how much interest will ana have earned on her savings account?

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.