I started today with CMPT 470 – Web based Information Systems at Simon Fraser University in Burnaby. The course will attempt to focus on all the web technologies popular today like XHTML, CSS, XML, databases, Ruby on rails, client-side/server-side scripting, etc and will entail going through a full project life-cycle involving internal group dynamics, business analysis, and final product delivery. Shareoint/WSS will be used for collaboration. I’m excited about this course because it will bring together everything that I have learned from the Web-Programming Associate Certificate course that I took at BCIT. The big project for the semester will be real-life driven with an attempt at presenting our finished product at an Open House at SFU sometime during the summer.
I have just finished some tutoring sessions with a bright Math 12 student, Jeanne, who was studying for some quizes and a provincial exam. We covered mainly Math 12 Statistics, including probability, permutations, and combinatronics. It was a challenge solving many of the questions that Jeanne needed help with but together, we were able to get through all of them. The questions that puzzled me the most was with regards to finding the probabilities of getting certain hands in a 5-card poker. Another question that gave me a tough time was about figuring out the probability of drawing a face card for the first card and a queen for the second card, when 2 cards are drwan without replacement from a 52-card deck. This took me up to 2am to figure out but it was well worth it. I’ll post the solution here in the hopes that it helps some other Math 12 student:
The solution is to find the sum of both of these two probabilities, giving us P(A or B):
P(A) = P(first card is a face card but NOT a queen and second card is a queen) and
P(B) = P(first card is a queen and second card is a queen).
Solving for P(first card is a face card but NOT a queen and second card is a queen):
There are three face cards in each suit, not counting aces, for a total of 12 face cards. The probability that the first card is a face card is then 12/52 but if we don’t count the queens, it’s 8/52. If the first card is not a queen then the probability of the second card being a queen is 4/51, i.e. there are four queens left in a deck of 51 cards. Total probability one face card (not a queen) and a queen is
P(first card is a face card but NOT a queen and second card is a queen)
= P(1st is face but NOT queen) * P(2nd is queen)
= 8/52 * 4/51
Now, solving for P(first card is a queen and second card is a queen):
The probability that the first card is a queen is 4/52 and the probability of the second card also being a queen out of a deck of 51 cards left is 3/51. Total probabilit of first card as queen and second card as queen is
P(first card is a queen and second card is a queen)
= P(1st is queen) * P(2nd is queen)
= 4/52 * 3/51
Therefore, P(A or B) gives us
= P(first card is a face card but NOT a queen and second card is a queen) + P(first card is a queen and second card is a queen)
= 0.012 + 0.0045
or is equal to 11/663 in your choice of answers.