# Counting rules in probability

Let me clarify lang why counting rules are used for this one:

Probabilities are calculated by (number of successful oucomes) divided by (number of all possible outocomes). So if you figure out these numbers then you get the right answer na. What complicates this question a bit is the fact that the whole procedure is made up of multiple tasks (the way you divide it is two tasks, (1) rolling two dice, (2) rolling two coins).

For example these are successful outcomes for a:

2,4,heads,heads

3,3,heads,heads

...

So you can count how many of these are there exactly. Thats when you use product rule:

task 1: rolling a sum of 6 for two dice, thats 5 unique ways

task 2: flipping two heads, thats 1 way

meaning there are (5)(1) successful outcomes.

While the total number of outcomes can be calculated using the product rule gihapon:

task 1: rolling any combination of dice rolls, thats 36 ways

task 2: flipping any combination of coin flips, thats 4 ways

meaning there are a total of (36)(4) outcomes.

So to calculate probabilities you divide:

(5)(1) / (36)(4)

Notice how this is the same outcome as multiplying both probabilities you got:

5/36 * 1/4 = (5)(1) / (36)(4)

Therefore for scenarios like these you multply the probabilities