please solve the questions below

Use the following information for all steps in this problem. Input all answers to three decimals places and do not input your answers as a percentage.

Alec is taking both a Statistics course and a Geography course this semester. The probability that he passes his Statistics course is 0.65. The probability that he passes his Geography course is 0.92. These two events (passing Statistics and passing Geography) are independent.

1. What is the probability he passes both classes?

2. What is the probability he passes, but fails the other?

3. What is the probability he passes at least.

4. What is the probability he passes neither class?

5. What is the probability he passes Statistics and fails Geography?

solve the question below giving explanations

6. What is the probability he passes Geography and fails Statistics?

Three prisoners, A, B, and C, are held in separate cells. Two are to be executed. The warder knows

specifically who is to be executed, and who is to be freed, whereas the prisoners know only that two

are to be executed. Prisoner A reasons as follows: my probability of being freed is clearly 1

3

until I

receive further information. However, it is clear that at least one of B and C will be executed, so I

will ask the warder to name one prisoner other than myself who is to be executed. Once I know which

of B and C is to be executed, either I will go free or the other, unnamed, prisoner will go free, with

equal probability. Hence, by asking the name of another prisoner to be executed, I raise my chances

of survival from 1

3

to 1

2

. Investigate A's reasoning. [Hint: find the conditional probability that A is

freed, given that the warder names B to be executed.]

In a particular geographic area, the lengths of human pregnancies from conception to birth follow an approximately normal distribution with a mean of 268 days and a standard deviation of 18 days. What is the probability that a pregnancy in this geographic area is more than 261 days In length? 0.5438 0.6517 0.6630 0.7598Question 28 [1 point] Amy is taking a statistics class and a biology class. Suppose her probabilities of getting a grade of A+ in statistics course is {135, grade of 11+ in biology is {121} and grade of A+ in both statistics and in biology is [1.11]. Find the probability that Amy will get at least one A+ between her statistics and biology classes. Table below gives the purchasing power of the dollar as measured by consumer prices according to the U.S. Bureau of Labor Statistics, Survey of Current Business. 0.531 0.565 0.556 0.544 0.530 0.512 Samce: US. Bureau of Labor Statistics. Survey of Current Business. a) Graph the data and obtain the trend line. b) Find the equation of the trend line. c) Estimate the consumer price in 2008 assuming the trend continues for 3 more years. (1) Find the correlation of coefficient (R-square)