Question 389991: I STARTTED, BUT DONT GET WHAT TO DO. i MISSED 3 WEEKS OF SHOOL BECUASE IF iLLNESS PLEASE EXPLAIN TO ME WHAT I AM SUPPOSED TO DO.
The setting. Amarillo Slim is at it again. Supposethat Slim has beendealt the Jack
of Spadesfrom a standard deck of playing cards. Then he is dealt four more cards
for a total of five cards. He wants to determinethe probability that he will end up
with exactly 3 jacks in his hand of five cards.
In this investigation, you will help Slim find the probability of having 3 jacks in his
hand by three different methods.
I Part 1. Do the experiment. With a partner, get a standarddeck of playing cards.
One person(playing the role of Slim) takes the jack of spades,and the other person
shuffles the remaining cards,and without either one looking, deals 4 more cards to
Slim. Make a chart like the one below, and use tally marks to record the number of
I times you endedup with exactly 3 jacks in your hand, and the number of times you
didn't. Each personshould do the experimentat least 10 times (20 would be better!),
and then changeroles -Slim becomesthe dealer, and the dealer becomesSlim.
.Combine
your results with those of other pairs in your classto obtain a much larger
r
number of repetitions. Then calculatethe proportion of times you ended up with
exactly 3 jacks in your hand from your 20 (or 40) repetitions. Also calculate the
proportion for the larger number of repetitions from the rest of the class. Theseproportions will be
approximations for the probability in question.
J
Part 2. Approximate the answer by meansof a simulation. Useyour TI-83/89 or one of the following statistics
utilities for the computer: Minitab, JMP, Data Desk, or Fathom,to simulate the experiment. Enter 51 numbers
into a variable or a list: four each of 1to 13, but with one 11 missing for the jack in your hand. Then sample 4
numbers from this list, and count the number of 11's. Whenthe number of II's from the sample of four cards is
2, then count that as a success. If you repeatthis severalthousandtimes, you should obtain a pretty decent
approximation for the probability of ending up with 3 jacks. Describethe process,and your results. Compare
your results from Part 1 with your results from this simulation.
Part 3. Find the theoretical probability. Find the theoretical probability of ending up with exactly 3 jacks.
Here's a hint: In how many ways can you gettwo of the remainingjacks? In how many ways can you get the
remaining two cards that are not jacks? Don't forget to divide by the total number of four-card hands from a 51
card deck. How close did you come to this theoretical result in parts I and 2?
The Report. Describe your investigation}n a report. Follow the conventionsas described in the general
guidelines for writing up Special Problems. You will be gradedon both the accuracy of your work and the
quality of your written communication. Seeyour teacherif you have questions.
Deadline. This Special Report will be due no later than
[Credits: Thanks to the following teacherswho indirectly suggested
this specialproblem: Stoney Pryor (A&M
Consolidated HS, TX) and Pat Ballew (Lakenheath,U. K.).]
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! This is quite a bit for most tutors to handle. If you don't know what you're supposed to do, I recommend you read (and reread) the instructions you provided, as they very clearly explain the procedures.
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