A little probability help? (1 Viewer)

1. Let X be the number of auto accidents in a neighborhood each month. Let the pmf of X be given by f(x) =1/(x+1)(x+2). Find the conditional probability that X≥3 given that X≥1.                                                 
                                                                                        
 2. A machine fills bags of potatoes to ten pounds. The probability that any given bag of potatoes is less than ten pounds is 0.04. We’ll check each bag to see if it is ten pounds. Let X be the number of bags checked until the first bag under ten pounds is found.                       
 (a) Find P(X = 20)                                                          
 (b) Find P(X > 20)                                                          
 (c) Find P(X < 20)        

                                              
3. A students take a quiz with eight multiple choice questions, each with five possible answers, only one of which is correct. Let X be the random variable corresponding to the first question correctly answered.

(a) Find the pmf f(x).                                                      
(b) Find E(X).

probably

Ben & Jerry's said:

1. Let X be the number of auto accidents in a neighborhood each month. Let the pmf of X be given by f(x) =1/(x+1)(x+2). Find the conditional probability that X≥3 given that X≥1.         

Click to expand...

f(0) = 0.5.  f(1) + f(2) = 0.25.  So f(3+) = 0.25, and the conditional probability is 0.5. 

Ben & Jerry's said:

 2. A machine fills bags of potatoes to ten pounds. The probability that any given bag of potatoes is less than ten pounds is 0.04. We’ll check each bag to see if it is ten pounds. Let X be the number of bags checked until the first bag under ten pounds is found.                       
 (a) Find P(X = 20)                                                          
 (b) Find P(X > 20)                                                          
 (c) Find P(X < 20)    

Click to expand...

P(X=20) = 0.96^19 * 0.04 ~= 0.0184.

P(X<20) = sum(0.96^(i-1) * 0.04) for i = 1..19.  ~= 0.5396.

P(X>20) = 1 - the above two results ~= 0.442.

Ben & Jerry's said:

3. A students take a quiz with eight multiple choice questions, each with five possible answers, only one of which is correct. Let X be the random variable corresponding to the first question correctly answered.

(a) Find the pmf f(x).                                                      
(b) Find E(X).

Click to expand...

Assuming the students are just guessing randomly...

f(x) = 0.8^(x-1) * 0.2

I forget how to do E(X) where there's a finite number of questions (so it's possible the student gets none of them correct).  Low-confidence guess is the answer is (1-0.8^8)/0.2 ~= 4.16. 

One of the two responses above is correct.