2. Suppose license plates have 6 entries. The first three entries must be letter

Question

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)

Explanation / Answer

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]

****************

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]

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

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