2 Suppose license plates have 6 entries The first three entr

2. Suppose license plates have 6 entries. The first three entries must be letters (A Z), and the last three must be digits(0 9). Letters and digits can be used more than once.

(a) A license plate is selected randomly. What is the probability that the letter Z is not used? ( Hint : It may help to first find the total number of possible license plates)

(b) Jen was born in February of ’88. She chooses a license plate by randomly ordering the letters J,E and N in the first three spots and randomly ordering the digits 2, 8, and 8 in the last three spots. What is the probability that Jen chooses a license plate with two 8’s adjacent?( Hint: It may help to first find the total number of possible license plates that jen can pick)

Solution

a)

Note that

P(a letter is not letter Z) = 25/26

Thus, for this to occur 3 times on the plate (no Z\'s),

P(no Z\'s) = (25/26)^3 = 0.888996359 [answer]

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b)

We need not care about the letters as those won\'t affect the numbers.

Here are the possible permutations of 2,8,8:

288
828
882

Of these three, two have the 8\'s adjacent.

Thus,

P(8\'s are adjacent) = 2/3 = 0.6666666667 [answer]