Consider the relation schema OrderContent$($orderID$,$ product, amount$)$

Let$$s assume the relation occupies $120$ pages of space.

On average, each order includes $5$ products and each product belongs to $30$ orders. There is no clustering of any attributes.

Two kinds of queries are frequent for the table: searching for certain order ID $($type Q$1,$ fraction p$1)$ and searching for orders with certain products $($type Q$2,$ fraction p$2).$

Insertions to the table take the fraction $1-$ p$1-$ p$2$ of all operations on the table $($type I$).$

Give formulas in terms of p$1$ and p$2$ to measure the cost of queries Q$1$ and Q$2$ and insertion I under the following four combinations.

$1.$ No indices at all

$2.$ Index for the attribute orderID

$3.$ Index for the attribute product

$4.$ Index for both attributes $($orderID and product$)$

Remember to also explain where the numbers in your formulas come from.