Question

Assume that we turn over 10 cards from the top of the shuffled deck and then we count the number of aces that were turned over. Determine whether the process describes a binomial random variable. If it is binomial, give values for n and p. If it is not binomial, state why not.

Answer 1

Yes it describe a binomial random variable.

Here p= 1/13 n= 10

Explanation:

Let us regard the turning over ten cards as an experiment. Then we observe that

1) each turning over a card has two possible outcomes ( ace ) success and

( not ace ) failure.

2) the probability of ace ( success) p = 1/13 and remain constant.

3) the successive turning of cards is independent.

4) the card is turned 10 times.

An experiment having the above characteristics is called a binomial experiment and the variable is called binomial random variable.

Here p= 1/13 n= 10