college statistics

Question

A random experiment was conducted where Person A tossed four coins and recorded the number of “heads”. Person B rolled two dice and recorded the smaller number out of the two dice. Answer the questions (either by direct computation or using simulations; use 10000 long columns).

I) Which of the two persons (A or B) is more likely to get the number “3”? (6.66 points)

a. Person A
b. Person B
c. Both persons have very similar probability of obtaining “3”
d. Not possible to determine
II). What is the probability that person B obtains number “5” or “6”? (6.66 points)

a. About 5%
b. About 11%
c. About 28%
d. About 35%
III) Which of these events are the most probable? (6.66 points)

a. Person A gets “3” and Person B gets “6”
b. Person A gets “2” and Person B gets “5”
c. Person A gets “3” and Person B gets “5”

Answer 1

This is a Binomial Distribution...

 

I)  Person A  we want the probability of 3 heads when n=4     and         p=.5         

 

                   Binpdf(n=4, p=.5 , p=3) = ₄C₃(.5)⁰(.5)^4-3= 4*1*0.0625 = 0.5

 

     Person B  we want the probability of 3 being the lower number of 2 dice.  This is probably easier to see if we list the

 

                    possible outcomes.  Note that each outcome has probability 1/36.

 

Die 1    Die 2        Die 1 Die 2        Die 1 Die 2        Die 1 Die 2        Die 1 Die 2        Die 1 Die 2

1          1              2        1            3          1          4          1           5         1           6        1                    

1          2              2        2            3          2          4          2           5         2           6        2

1          3              2        3            3          3          4          3           5         3           6        3

1          4

1          5

1          6

 

Finish this chart.  Then count the number of times that 3 is the smaller number.   That should be multiplied by 1/36 to find the probability.

 

The other 2 problems can be worked out similarly.

 

Let me know if you have more questions!