Compute $\frac{3}{4}\cdot \frac{8}{9}\cdot \frac{15}{16}\cdot \frac{24}{25}\cdot \frac{35}{36}\cdot \frac{48}{49}\cdot \frac{63}{64}\cdot \frac{80}{81}\cdot \frac{99}{100}$. Express your answer in the simplest way possible. (Suggestion: First, try computing $\frac{3}{4}\cdot \frac{8}{9},$ then $\frac{3}{4}\cdot \frac{8}{9}\cdot \frac{15}{16},$ and so on. Look for patterns.)

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

it would be 6xy and -16xy.