Part$($A$)$

Given information:

There are two variables X and Y$.$

We want to find the probability that Y is greater than $7,$ given that X is between $100$ and $130$ grams.

There is a table with counts of occurrences for different combinations of X and Y values.

Steps to find the Probability:

$1.$ Define the event:

The event we are interested in is Y $>7,$ Meaning, Y is either in the class

$7,8,9,$ or $10,11,12$

$2.$ Identify the relevant entries in the table:

We need to focus on the entries where X is between $100$ and $130$ grams. These Entries represent the relevant subset of the data.

$3.$ Count total occurrences:

Add up The occurrences for X between $100$ and $130$ grams. The sum is $1093+1272=2365$

$4.$ Count occurrences where Y$>7$:

From the relevant subset of data, count the occurrences where Y is Greater than $7.$ in this case It's in the classes.

$7,8,9,$ or $10,11,12$ the count is $1272.$

$5.$ Calculate probability.

Use the counts from steps $3$ and $4$ to calculate the conditional probability using the formula.

between $[100,130])=$

Substitute the values P$($Y $>7|$X Between $[100,130])=$

$0\mathrm{.}538$

$6.$ Calculate the result:

Perform the calculation: P$($Y $>7|$X Between $[100,130])$

$0\mathrm{.}538$

Explanation:

Conclusion: The probability that Y is greater than $7$ given that X is between $100$ and $130$ grams, is approximately $0\mathrm{.}538$

This means that within the specified range of X values, there is$.$ about a $53\mathrm{.}8\%$ Chance that Y will be greater than $7.$please explain thefirst $3$ steps how total occurence is calculated?