SOLUTION: A number is picked at random from the digits 1, 2, ..., 9. Given that the number is a multiple of 3, find the probability that the number is (a) even, (b) a multiple of 4.

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Question 1203254: A number is picked at random from the digits 1, 2, ..., 9. Given that the number is a multiple of 3, find the probability that the number is
(a) even,
(b) a multiple of 4.
Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.
A number is picked at random from the digits 1, 2, ..., 9.
Given that the number is a multiple of 3, find the probability that the number is
(a) even,
(b) a multiple of 4.
~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

(a)  The space of events consists of 9 elements (all with the uniform probability of 1/9}.

     The reduced set, where you are looking for, consists of 3 elements {3, 6, 9 }.

     The set of favorable elements is {6}, consisting of 1 element.

     The probability is the ratio P = .    ANSWER



(b)  In this case, the space of favorable elements is EMPTY.

     Therefore, the probability is 0 (zero).    ANSWER

Solved.



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