Determine whether the variable X has a binomial distribution in each of the following cases. If it does, explain why and determine the values of the parameters n and p. If it doesn't, explain why not.

1. You select one row in the random digits Table B from the textbook.
X = number of 8's in the row
2. A fair die is rolled five times.
X = number of times the number 3 is observed.
3. A boy asks the same girl to go on a date every day for a week.
X = number of times the girl agrees to go on a date with the boy

Question

Determine whether the variable X has a binomial distribution in each of the following cases. If it does, explain why and determine the values of the parameters n and p. If it doesn't, explain why not. 

1. You select one row in the random digits Table B from the textbook. 
X = number of 8's in the row 
2. A fair die is rolled five times. 
X = number of times the number 3 is observed. 
3. A boy asks the same girl to go on a date every day for a week.
X = number of times the girl agrees to go on a date with the boy

anonymous · Answer

2. A fair die is rolled five times. X = number of times the number 3 is observed.  
is binomial for sure

anonymous · Answer

all the probabilities are $\frac{1}{6}$ so $p=\frac{1}{6}$ and $n=5$

anonymous · Answer

A boy asks the same girl to go on a date every day for a week. X = number of times the girl agrees to go on a date with the boy
seems unlikely since it is doubtful that saying "yes" is an independent event