Final answer:
To find the probability of being dealt a "threes over sixes" fullhouse, calculate the number of favorable outcomes and divide by the total number of possible outcomes.
Step-by-step explanation:
To find the probability of being dealt a "threes over sixes" fullhouse (three threes and two sixes), we need to first find the number of outcomes favorable to the event and then divide it by the total number of possible outcomes.
In a deck of 52 playing cards, there are 4 threes and 4 sixes. To form a full house, we need to choose 3 threes out of 4 and 2 sixes out of 4, which can be calculated using combinations. The total number of ways to choose the two different ranks is 4C3 * 4C2 = 4 * 6 = 24.
The total number of ways to deal a 5-card hand from a deck of 52 cards is 52C5 = 2,598,960.
Therefore, the probability of being dealt a "threes over sixes" fullhouse is 24/2,598,960, which is approximately 0.00000922.