Kyle has three short straws, four medium straws, and six long straws. If he randomly draws two straws, one at a time without replacement, what is the probability that both are short straws?
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lets call these SSS MMMM LLL LLL for short , medium and long
so the first straw, you have a probability of 3 / 13 of picking a short straw.
the next straw, now you only have 12 straws since you already picked a short straw from last choice. so now you have 2/ 12 of picking a short straw
so 3/13 * 2 / 12
more generally, the probability of the conjunction (AND) of two events is
P ( A & B ) = P ( A) * P ( B | A) ,
P(B|A) means the probability of given that A has occurred already. So here we have
probability ( short straw on first draw & short straw on second draw) = P(straw on first draw) * P(straw on second draw given first straw was a short one)