Question

1. Determine whether the following procedures results in a binomial distribution. If not, state which requirement it does not satisfy.                                               (4)      
   1. Selecting three cards (with replacement) from a well-shuffled deck of playing cards and keeping track of red or black card.
2. 2. Rolling a six-sided die 5 times and keeping track of all the numbers rolled.

Answer 1

where p= probability of success in a trial and q=1-p =probability of failure

n= number of independent trials. Here x=0,1,2,..........n.

1. here probability of success=probability of red or black card= 1 since in a deck of 52 cards we have 26 red 26 black cards. so any randomly selected card will be either red or black. so here is no question of failure so q=0 so here we can not use Binomial distribution.

2. Here since we are keeping track of all numbers rolled so there is no question of probability of success p and probability of failure q=1-p here q=0 so we can not use binomial distribution here.