SOLUTION: I need help understanding how solve these types of problems...can someone explain them to me thanks... 1) two 6 sided dice are rolled. What is the probability that the sum of th

Question 88341: I need help understanding how solve these types of problems...can someone explain them to me thanks...
1) two 6 sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 9?
2) what i sthe probability that at least 2students in a class of 36 have the same birthday?
3) Consider determining how many possible phone numbers are in an area code (repeated numbers allowed). Is this a combination, a permutation, or neither? Provide an appropriate response.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1) two 6 sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 9?
You should sketch the sample space (results of the experiment) as a 6x6 square
with 1,2,3,4,5 6 on the left side and again on the top.
Fill in the 36 entries on the square as the sum of the row and column the
square is in. You will get 36 entries that range from 2 to 36
Count the number of entries that are greater than 9; then divide by 36
That is the probability you are looking for.
Answer = 6/36 = 1/6
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2) what is the probability that at least 2 studentsin a class of 36 have the same birthday?
The probability you and your mother share the same birthday is 1/365;
Prob(2 or more of 36 have the same birthday) + P(no two have the same birthday )
= 1
---------
P(2 or more of 36 have the same birthday) = 1-P(no two have the same birthday)
-------
Prob(no two have the same birthday) = (365/365)(364/365)(363/365)...(330/365)
---------
Therefore Prob (2 or more have the same birthday) = 1-[(365!/329!)*1/365^36]

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3) Consider determining how many possible phone numbers are in an area code (repeated numbers allowed). Is this a combination, a permutation, or neither? Provide an appropriate response.
I assume by "in an area code" means the number of 7-digit phone numbers
possible associated with a particular area code.
If that is so you have 10 ways to choose each of the 7 digit positions
since repetition is allowed. That is not a combination because you are
not choosing groups that have no same elements; it is not a permutation
because you are not choosing the various arrangement of 10 digits; it is
an application of the general counting priciple which says "if step one
of a process can be performed in n ways and step two can be performed in
m ways,then the two steps can be performed in n*m ways". Your answer is
10^7
=============
Cheers,
Stan H.
Stan
permutation

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