Suppose that Mahmoud simultaneously rolls a pair of fair $6$-sided dice. Let $A$ be the event that the first die is $2$ or greater and $B$ be the event that the second die is $1$. Use the sample space of possible outcomes below to answer each of the following questions. **What is $P(A)$, the probability that the first die is $2$ or greater?** [[☃ input-number 1]] **What is $P(B)$, the probability that the second die is $1$?** [[☃ input-number 2]] **What is $P(A\text{ | }B)$, the probability that the first die is $2$ or greater, given that the second die is $1$?** [[☃ input-number 3]] **What is $P(B\text{ | }A)$, the probability that the second die is $1$, given that the first die is $2$ or greater?** [[☃ input-number 4]] **What is $P(A\text{ and }B)$, the probability that the first die is $2$ or greater and the second die is $1$?** [[☃ input-number 5]] **What is $P(A)\cdot P(B\text{ | }A)$?** [[☃ input-number 6]] **What is $P(B)\cdot P(A\text{ | }B)$?** [[☃ input-number 7]] $\qquad$