Writing Assignment Three
A,D,E,F,G

A) The probability that you are dealt pocket aces is 1/221, or .00452 to three significant digits. If you studied either sections 4.5 or 4.6 of section 4.8, verify that probability. calculated as follows: P = f/N where f is the number of ways an even can occur, and N is the total number of possible outcomes. For the first Ace the probability is 4/52 as there are 4 Aces and 52 total cards in a deck. For the second Ace the probability is 3/51 as there are now 3 Aces and 51 total cards left in the deck. Because these two events are independent, we use the Special Multiplication Rule. Therefore, 4/52 x 3/51 = 12/2652, which is simplified to 1/221 or 0.00452.

B) Using the result from part (A) obtain the probability that you are dealt "pocket kings"

C= first card is a king
D= second card is a king

P(C)= 4/52
P(D|C)= 3/51
P(C&D)= (4/52) *( 3/51) = 12/2652= 1/221 = .00452
P(C&D)=P(A&B)
.452% chance

C) Using the result from part (A) and your analysis in part (B), find the probability that you are dealt a "pocket pair", that is, two cards of the same denomination.

In all of these, depending on the first event, there are only 3 possible ways for the second event to happen. However for this calculation the probability of the first event doesn't matter due to fact that you can pick any of the 52 cards.

E = pocket pair

P(E)= 3/51= .0588
5.88%

D) Assuming that you are dealt a "pocket pair", determine the probability that the flop contains at least 1 card of your denomination.

Using the Complementation Rule: P(getting the same #) = 1 – P(not getting the same #)P(not getting the same #) = 48/50 because there will be 50 cards left in the deck, and 48 of them will be different than the number in the pair you were dealt. Therefore: P(getting the same #) = 1 – 48/50 = 1 - .96 = .04 = 4%

E) Assuming that you are dealt a "pocket pair", determine the probability that the flop gives you "trips", that is contains exactly 1 card of your denomination and two other unpaired cards.
P(being dealt card of your denomination) x P(any other card) x P(any other unpaired card) = 2/50 x 48/49 x 44/48 = 4224/117600 = .0359 = 3.59%
The probability of being dealt a card of your denomination is 2/50 as calculated above.
The probability of being dealt any other card is 48/49 because there are 49 total cards left in the deck, and 48 of them are different from the cards you were dealt. The probability of being dealt any other unpaired card is 44/48 because there will be a total of 48 cards left in the deck, and 44 will be different from the previous two cards (1 left of the original denomination and 3 left of the denomination of the card that was just chosen, 48 – 1 – 3 =44).
Answer= .0359 = 3.59%

F) Assuming that you are dealt a "pocket pair", determine the probability that the flop gives you "quads" that is, contains 2 cards of your denomination.
P(being dealt card of your denomination) x P(being dealt card of your denomination) x P (being dealt any other card) = 2/50 x 1/49 x 1 = 2/2450 = .0008 = .08%
The probability of being dealt a card of your denomination is 2/50 as calculated in d. The probability of being dealt the last card of your denomination is 1/49 because there are 49 total cards left in the deck, and only 1 is left of your denomination. The probability of being dealt any other card is 1 because it is a certain event.
Answer = .0008 = .08%

G) Assuming that you are dealt a "pocket pair", determine the probability that the flop gives you a "boat", that is, contains 1 card of your denomination and 2 cards of another denomination.

P(being dealt card of your denomination) x P(any other card) x P(card of same denomination as previous) = 2/50 x 48/49 x 3/48 = 288/117600 = .002 = .24%
The probability of being dealt a card of your denomination is 2/50 as calculated in d. The probability of being dealt any other card is 48/49 because there are 49 total cards left in the deck, and 48 of them are different from the cards you were dealt. The probability of being dealt a card of the same denomination as the previous is 3/48 because there will be a total of 48 cards left in the deck, and 3 left of the same denomination.
Answer= .002 = .24%