A Number Between 1 and 10, Inclusive, Is Randomly Chosen $$\text { Find } P ( A \mid B ) \text { and } P ( B \mid A ) \text {. }$$

question 24

Essay

A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows.
A: {The number is even}
B: {The number is less than 7} $$\text { Find } P ( A \mid B ) \text { and } P ( B \mid A ) \text {. }$$

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Definitions:

\(n + 1\)

An expression representing one more than a given number \(n\).

\(( n + 6 ) !\)

A notation indicating the factorial of n plus 6, meaning the product of all positive integers up to n+6.

\(( n + 3 ) !\)

Denotes the factorial of the sum of a variable n and 3, representing the product of all positive integers up to and including (n+3).

\(n !\)

Denotes the factorial of n, which is the product of all positive integers less than or equal to n.