I really need help on this question. When dealing out a game of thirteen, what is the probability of getting an insta-win. This of course includes a bomb of 2s, a 12 long straight, and any other insta-wins that are present in the game. Please answer because I need to finish a stats project by monday.
To calculate the probability of an insta-win in the game of thirteen, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Let's start by identifying the possible outcomes. In a game of thirteen, there are 13 cards ranging from Ace to King in each of the four suits, totaling 52 cards in a standard deck.
Now, let's consider the different types of insta-win conditions:
1) Bomb of 2s: A bomb of 2s refers to having all four 2s in your hand. There are four 2s in the deck, so the probability of getting a bomb of 2s is (4 choose 4) divided by (52 choose 13).
2) 12-long Straight: A 12-long straight refers to having any combination of cards from Ace to Queen in any suit, along with one additional card. Since there are four suits, there are four possible 12-long straights (one for each suit). In each suit, there are (12 choose 12) ways to choose the 12 cards and (40 choose 1) ways to choose the additional card. Therefore, the total number of favorable outcomes for a 12-long straight is 4 * (12 choose 12) * (40 choose 1).
To calculate the overall probability of an insta-win, add up the number of favorable outcomes for each condition and divide it by the total number of possible outcomes:
Probability of an insta-win = (Number of favorable outcomes) / (Total number of possible outcomes)
Note that there may be additional insta-win conditions in the game of thirteen, depending on the specific rules you are following. Make sure to include those as well in the calculation if they exist.
Please let me know if you need any further assistance!