What is the probability that a number selected from the numbers 1 2 3 15 is a multiple of 3 *?

The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is

`(A)4/15`

`(B)2/15`

`(C)1/5`

`(D)1/3`

Correct answer: C
The multiples of 4 between 1 and 15 are 4, 8 and 12. The probability of getting a multiple of `4=3/15=1/5`

Concept: Basic Ideas of Probability

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Answer

Hint: Here, we will be proceeding by evaluating how many numbers out of the given 15 numbers are a multiple of 4 and then the required probability is easily determined with the help of the general formula for probability of occurrence of an event. Complete step-by-step answer:Given, the numbers are 1,2,3,4,5,6,7,8,9,10,11,12,13,14 and 15As we know that the general formula for probability is given byProbability of occurrence of an event$ = \dfrac{{{\text{Number of favourable cases}}}}{{{\text{Total number of possible cases}}}}$Here, the event is that we have to select a number from the given 15 numbers such that the selected number is a multiple of 4.So, the favourable event is that the selected number is a multiple of 4.From the given 15 numbers, the numbers that are multiple of 4 are 4,8 and 12.Here, Number of favourable cases = Total number of numbers (out of the given numbers) that are multiple of 4 = 3Total number of possible cases = Total number of given numbers = 15Therefore, Probability that a number selected is a multiple of 4 $ = \dfrac{{\text{3}}}{{{\text{15}}}} = \dfrac{1}{5}$.Hence, $\dfrac{1}{5}$ is the probability that a number selected from the numbers 1,2,3, ……,15 is a multiple of 4.Note: In this particular problem, the numbers which are multiple of 4 are the numbers which are exactly divisible by number 4 (i.e., the numbers which are when divided by 4 does not leave any remainder). Here, the possible cases include all the 15 given numbers because when a number is selected at random out of these 15 numbers, anyone of them can occur.