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