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(C) The set of possible values for $p$ and $q$ is $S = \{1, 2, 3, 4, 5, 6\}$.The total number of pairs $(p, q)$ is $6 	imes 6 = 36$.We need to find t

Vedclass · Accepted Answer

$11/23$

Vedclass · Answer

(C) The set of possible values for $p$ and $q$ is $S = \{1, 2, 3, 4, 5, 6\}$.The total number of pairs $(p, q)$ is $6 	imes 6 = 36$.We need to find the number of distinct rational numbers $p/q$.The distinct values are:$1/1=1, 1/2, 1/3, 1/4, 1/5, 1/6$$2/1=2, 2/2=1, 2/3, 2/4=1/2, 2/5, 2/6=1/3$$3/1=3, 3/2, 3/3=1, 3/4, 3/5, 3/6=1/2$$4/1=4, 4/2=2, 4/3, 4/4=1, 4/5, 4/6=2/3$$5/1=5, 5/2, 5/3, 5/4, 5/5=1, 5/6$$6/1=6, 6/2=3, 6/3=2, 6/4=3/2, 6/5, 6/6=1$Listing the distinct values: $\{1, 2, 3, 4, 5, 6, 1/2, 1/3, 1/4, 1/5, 1/6, 2/3, 2/5, 3/2, 3/4, 3/5, 4/3, 4/5, 5/2, 5/3, 5/4, 5/6, 6/5\}$.Counting these,we find there are $23$ distinct rational numbers.$A$ proper fraction is a fraction where $p The proper fractions are: $\{1/2, 1/3, 1/4, 1/5, 1/6, 2/3, 2/5, 3/4, 3/5, 4/5, 5/6\}$.There are $11$ such distinct proper fractions.Thus,the probability is $11/23$.

$A$ rational number is selected at random from the distinct rational numbers of the form $p/q$ formed with $p$ and $q$ belonging to the set $\{1, 2, 3, 4, 5, 6\}$. The probability that the rational number selected is a proper fraction is:

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