Free Critical Thinking On Paper

There two ways to verify to verify the probability of being dealt with pocket aces is 1/221. The first method is the use of permutation and combination. In this method, we calculate the number of possible ways of arranging two aces out of 52 cards as the first step. The next step is determining possible number of ways of arranging 2 aces out of four cards. The above permutations are shown below.
51*522=1326 (i)
4*32=6 (ii)
Getting the probability of being dealt two pocket aces is therefore the result of equation (ii) divided by the result of equation (i), which works out as
61326=1221
The other method of arriving at the same probability is by use of decision tree where the cards are dealt without replacement. There are four aces in a pack of 52 cards. This makes it 4 ways out of 52 to obtain an ace. After the first ace has been obtained, there remain 3 aces out of 51 cards. Therefore, the probability of obtaining the second ace is 3 out of 51. The probability of getting two aces in the product of obtaining the first ace and the second ace.
=152*352=1221
The probability of being dealt pocket kings is the same as of pocket aces. The number of cards is the same and there are as many kings as there are aces in a pack of 52 cards. The probability of pocket kings is therefore 1/221
Similarly, the probability of being dealt any pocket pair is still 1/221. This is because there are four cards of each denomination in a pack of 52 cards and procedure of calculating the probability of any pocket pair follows that of pocket aces.
The probability of getting at least more card of your combination is (1-the probability of getting no card similar to your pair). Since one already has a pair from the pack of 52, there remain two more card similar to the he/she holds. The probability of not picking the remaining pair in three picks is=4850*4749*4648 . The probability of at least having one card similar to the your pair is
- (=4850*4749*4648).
- 0.882449= 0.117551
The probability of a flop giving “trips” is 250*4849*4448or4850*4449*248 . The first fraction is the probability of picking a card similar to the pair. The second fraction is the probability of picking a card not similar to the pair while the third fraction represents the probability of picking a card neither similar to the pair nor to the second pick After the “or” The first fraction is the probability of picking a card not similar to the pair. The second fraction is the probability of picking a card neither similar to the pair nor to the second pick not similar to the pair while the third fraction represents the probability of picking a card similar to the pair. The probability of “trips” is therefore 0.071837.
The probability that the flop gives you one card of your denomination and another two cards of another denomination is 250*4849*348or4850*349*248 . The first fraction is the probability of picking a card similar to the pair. The second fraction is the probability of picking a card not similar to the pair while the third fraction represents the probability of picking a card similar to the second pick. After the “or”, the first fraction is the probability of picking a card not similar to the pair. The second fraction is the probability of picking a card similar to the first pick while the third fraction represents the probability of picking a card similar to the pair. The probability of a “ boat” is therefore 0.004898