Answer:
128 posibilities
Step-by-step explanation:
We have 7 colleges (A,B,C,...,H) which form a set with seven elements.
What you are asking is the number of elements (or cardinality) of the set that contains all possible sets formed by those 7 elements (or the "power set").
It is known that if n is the number of elements of a given set X, then the cardinality of the power set is .
Therefore, there are or 128 possibilities (or elements) for the set of colleges that he applies to.
Answer:
c. The number of 7's in a randomly selected set of five random digits from a table of random digits.
True, for this case we have a value fixed for n =5 and the probability is defined for each number 1/10 assuming numbers (0,1,2,3,4,5,6,7,8,9) so then the random variable "The number of 7's in a randomly selected set of five random digits" can be modelled with the binomial probability function.
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
The conditions to apply this distribution is that we have the parameters fixed n and p.
Let's analyze one by one the possible solutions:
a. The number of traffic tickets written by each police officer in a large city during one month.
False, the number of traffic tickets written by each police is not a fixed amount always, so then the value of n change and we can't apply a binomial model for this case.
b. The number of hearts in a hand of five cards dealt from a standard deck of 52 cards that has been thoroughly shuffled.
False, not all the hands of size 5 are equal and since we can't ensure this condition then the binomial model not apply for this case
c. The number of 7's in a randomly selected set of five random digits from a table of random digits.
True, for this case we have a value fixed for n =5 and the probability is defined for each number 1/10 so then the random variable "The number of 7's in a randomly selected set of five random digits" can be modelled with the binomial probability function.
d. The number of phone calls received in a one-hour period.
False, the number of phone calls change by the hour and is not always fixed so then we don't have a valu for n, and the binomial model not applies for this case.
e. All of the above.
False option C is correct.