*Suppose license plates consist of two letters from 26 English letters followed
ID: 3355985 • Letter: #
Question
*Suppose license plates consist of two letters from 26 English letters followed by three digits from 0,1,2,...,9 (letters and digits can be repeatedly used). Suppose all possible combinations have been used. If you select a car at random, what is the probability that the plate has (a) both letters the same. (b) two letters are distinct but all digits the same. (c) only even digits.
*A box contains six red and four blue marbles. Two marbles are drawn from the box (without replacement) and their colors are noted. Dene the following events. A: The rst marble is red. B: The second marble is red. (a) Find P(A); P(A); P(A B); P(B); P(BjA); P(AjB): (b) Determine of A and B are independent.
Explanation / Answer
(a) There are 26 letters and hence there can be 26 repetitions of letters.
The three digits thereafter can come in 10 * 10 * 10 = 1000 ways.
Therefore there are 26000 possible numbers.
=> Probability that the plate has both letters the same = 26000 / 676000 = 1 / 26 = 0.0385.
(b) The two different letters can come in 26 * 25 ways and the three same digits in 10 ways. There are 6500 numbers.
=> Probability that the two letters are distinct but all digits the same = 6500 / 676000 = 0.0096.
(c) There are 5 even digits. The number of plates = 26 * 26 * 5 * 5 * 5 = 84500.
=> Probability that there are only even digits = 84500 / 676000 = 0.125.
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