A whole number from 1 to 15 inclusive is picked at random.
E = Whole numbers from 1 to 15 inclusive
M = Multiples of 3
By correctly completing the
F = Factors of 24
(Venn diagram)
a) What is the probability
that the number chosen
is a multiple of 3 given
that it is a factor of 24?
b) What is the probability
that the number chosen
is a factor of 24 given
that it is a multiple of 3?

The probability for the scenario in a and b are; 1/5 and 1/5 respectively.

The set of numbers which make up the universal set are: {1, 2, 3 ,4 ,5 ,6 ,7, 8, 9, 10, 11, 12, 13, 14, 15}

The numbers in the common to both subsets M and F are: 3, 6, 12

a) The probability that the number chosen

is a multiple of 3 given that it is a factor of 24 is therefore;

b) the probability that the number chosen is a factor of 24 given that it is a multiple of 3 is therefore;

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Explanation:

The figure attached shows the Venn diagram for the given sets.

a) What is the probability that the number chosen is a multiple of 3 given that it is a factor of 24?

From the whole numbers 1 to 15, the multiples of 3 that are factors of 24 are in the intersection of the two sets: 3, 6, and 12.

There are a total of 7 multiples of 24, from 1 to 15.

Then, there are 3 multiples of 3 out of 7 factors of 24, and the probability that the number chosen is a multiple of 3 given that is a factor of 24 is:

b) What is the probability that the number chosen is a factor of 24 given that it is a multiple of 3?

The factors of 24 that are multiples of 3 are, again, 3, 6, and 12. Thus, 3 numbers.

The multiples of 3 are 3, 6, 9, 12, and 15: 5 numbers.

Then, the probability that the number chosen is a factor of 24 given that is a multiple of 3 is: