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Pin Numbers A student loan administrator distributes pin numbers to its debtors. Each pin consists of two letters followed by three numbers. (Assume repetition is allowed, and order is important.) (a) How many different pin numbers are there? (b) What is the probability a pin number selected at random ends in 000? (c) What is the probability a pin number selected at random begins with AA?

Puppies of the Dow Refer to Problems 41 and 43. (a) If five stocks from the Dogs of the Dow list are randomly selected, what is the probability all five will be Puppies of the Dow? (b) If five stocks from the Dogs of the Dow list are randomly selected, what is the probability exactly three will be Puppies of the Dow? (c) If five stocks from the Dogs of the Dow list are randomly selected, what is the probability at least two will be Puppies of the Dow?


40. Hockey There are 15 teams in the Eastern Conference of the National Hockey League for the 2009–2010 season, divided

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barnuts

I will just answer the problem about Pin numbers because the other questions lack other given values.

a. How many different pin numbers are there?

There are 26 letters in total and 10 numbers in total (including zero), therefore the total number of different pin numbers are:

Total possible = 26 * 26 * 10 * 10 * 10

Total possible = 676,000 different pins

 

b. What is the probability a pin number selected at random ends in 000

The total possible numbers with ending of 0 0 0 is:

Possible numbers = 26 * 26 * 1 * 1 *1

Possible numbers = 676

 

Therefore the probability is:

Probability = 676 / 676,000

Probability = 0.001 = 0.10%

 

c. What is the probability a pin number selected at random begins with AA?

The total possible numbers starting with A A is:

Possible numbers = 1 * 1 * 10 * 10 * 10

Possible numbers = 1000

 

Therefore the probability is:

Probability = 1000 / 676,000

Probability = 1.48 x 10^-3 = 0.148%

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