In Exercises 15 and 16 use the following information. the telephone numbers for
ID: 3177608 • Letter: I
Question
In Exercises 15 and 16 use the following information. the telephone numbers for a region of a state have an area code of 570. the next seven digits represent the local telephone numbers for that region. A local telephone numbers cannot begin with a 0 or 1. Your cousin lives within the given area code. What is the probability of randomly generating your cousin's telephone numbers on the first try? What is the probability of not randomly generating your cousin's telephone numbers on the first try? in Exercises 17 and 18 use the table which shows the number of students who took the July 2012 California Bar Examination for the frost time and the number of student who repeated the exam.Explanation / Answer
Answer to question # 15)
There are total of 10 digits from 0 to 9
we need to fill the seven blanks with these digits
since nothing is mentioned whether a digit can be repeated or not, we may assume it to repeat
The first digit cannot be 0 or 1, so it is left out with 8 favorable options: 2,3,4,5,6,7,8,9
[Since it is not mentioned in the question that the digits used in the state code must not be used, we are using them as well to form a local number]
Thus the number of ways in which a local number can be formed is as follows:
For first digit there are 8 options, for rest of the following 6 digits the number of options are 10 for each of them
thus total number of ways = 8 * 10* 10 * 10 * 10 * 10 *10 = 8000000 ways
.
Now the cousin may have any one specific combination out of these 8000000 numbers
Thus the probability of getting the cousins number = 1/8000000
P(generating cousin's number) = 1/8000000 = 0.000000125
.
Answer to question# 16)
Since the probability of randomly generating cousin's number = 1/8000000
The probability of NOT randomly generating cousin's number = 1 - 1/8000000 = 7999999/8000000
Thus P(generating cousin's number) = 7999999/8000000 = 0.999999875