You are traveling to Chicago to meet a friend. Upon arriving there, you realize

Question

You are traveling to Chicago to meet a friend. Upon arriving there,
you realize that your friend forgot to show up at the airport to pick you up. To
make matters your cell phone decides that this is the best time to stop
working. You want to call your friend, but cannot remember his phone
number. However, after some thought you remember that the last four digits
of his phone number are 8636. Further, a helpful but knowledgeable stranger
tells you that all local telephone numbers start with 4, 6, 7 or 9. Considering
that you have plenty of time on your hands, you decide to try all possible
combinations.
If each local phone call costs 10cents and you have $15 to spend on the
telephone calls, what is the probability that you will be able to call your friend
before your money runs out?

Explanation / Answer

We know the last four digits, so we only need to find the first three.
What we are looking for is the number of all possible sets of the first three digits (also called permutations), we can find this by finding the product of the possibilities for each individual spot:
We know that the first digit is 4,6,7, or 9, so there are 4 possible numbers
The second and third digit can be any single digit 0,1,2,3,4,5,6,7,8, or 9, so there are 10 possibilities for each.
Thus the total number = 4 * 10 * 10 = 400.
Since you have $15.00, the total number of phone calls you can make at $0.10 per call is 150.
Then the probability that one of your 150 calls is your friend's number, is 150/400=15/40=.375=37.5%

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.