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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Scott (Customer)

[00:00:00] At a distance of 100 yards, Mr. Winchester hits the target an average of 60% of the time. In a local rifle contest, each contestant will attempt 3 shots and receive the following reward depending upon the number of targets that he hits: $50 for all 3 targets; $25 for 2 targets; and $10 for 1 target. If a contestant misses all 3 targets, he must pay $100. Should Mr. Winchester enter the contest if he wishes to maximize his expected net gain?

Paul B (Tutor)

[00:00:14] hello

Scott (Customer)

[00:00:19] hello

Paul B (Tutor)

[00:00:27] good problem here.

[00:00:33] let's break it down

Scott (Customer)

[00:00:39] yea, I don't even know how to
set it up

Paul B (Tutor)

[00:01:36] first, we need to calculate the expected value of playing this game from Mr. winchester's point of view

[00:01:46] this is a discrete variable problem.

[00:02:28] assume independence for each shot

[00:03:49] does this look familiar

Scott (Customer)

[00:03:48] why .4?

[00:03:58] no

Paul B (Tutor)

[00:04:06] .4 is the probability of him missing the target

Scott (Customer)

[00:04:11] check

Paul B (Tutor)

[00:04:43] if X = 3, then he hit the target on all 3 shots, well this will happen .6x.6x.6

Scott (Customer)

[00:05:14] ok

Paul B (Tutor)

[00:05:40] so here we go with some calculations. stand by

[00:06:16] he has a .216 probability of hitting all three times

[00:06:24] makes sense

Scott (Customer)

[00:06:26] yes

Paul B (Tutor)

[00:06:55] so he will win 50 dollars with .216 probability

[00:07:16] if we multiply those 2 numbers, this will be the expected value of x = 3

[00:07:54] now if he hits 2 out of 3 targets, he wins 25 dollars

Scott (Customer)

[00:08:00] why only 50 and not 150?

[00:08:26] never mind, i got it

Paul B (Tutor)

[00:08:29] the problem states he will win 50 dollars if he h

[00:08:31] ok

[00:09:25] he has a .432 probability of getting x to be 2, which would give him 25 dollars.
so the expected count of x =2 is

Scott (Customer)

[00:09:39] ok

Paul B (Tutor)

[00:10:00] we do the same thing for x =1 and x = 0

[00:10:18] we will get this large sum and we will hope this sum is over 100 dollars

[00:10:26] let's continue with the calculations

Scott (Customer)

[00:10:30] ok

Paul B (Tutor)

[00:12:45] mr. winchester should play this game as he stands to make 18 dollars and 8 cents on average

Scott (Customer)

[00:13:54] please explain the last part (- 100 (.064)

Paul B (Tutor)

[00:14:15] of course, he misses all 3 times, x = 0

[00:14:37] so if he misses all 3 times, he has to pay 100 dollars.
it's negative because this is money out of his pocket

Scott (Customer)

[00:15:03] ok, i understand.. thanks for
your patience

Paul B (Tutor)

[00:15:18] i have a few questions for you know

[00:15:19] now

Scott (Customer)

[00:15:22] ok

Paul B (Tutor)

[00:15:33] do you understand where the 3 came from under x = 2

Scott (Customer)

[00:16:09] yes, that's the probabliity of
him making all three shots

Paul B (Tutor)

[00:16:27] no the 3 under x = 2

[00:16:49] where the arrow was drawn to

Scott (Customer)

[00:17:10] I thought that was part of the
probability

[00:17:29] no, that's how many shots he
takes

Paul B (Tutor)

[00:17:37] this is a binomial problem

Scott (Customer)

[00:17:42] ?

Paul B (Tutor)

[00:17:49] how many ways can he make 2 out of 3 shots

Scott (Customer)

[00:18:03] explain

Paul B (Tutor)

[00:18:05] I'm going to show you something from the internet stand by

[00:19:40] I'm working on this...

Scott (Customer)

[00:20:03] ok

[00:22:01] ok, if you have 3 shots (n trials) and there are only 2 outcomes (success and failure) and the probability of success is constant, you have a binomial variable

Scott (Customer)

[00:22:17] ok

Paul B (Tutor)

[00:22:22] what i have highlighted probably looks familiar

Scott (Customer)

[00:22:35] i dont see anything on my
screen

Paul B (Tutor)

[00:22:53] is the screen totally blank

Scott (Customer)

[00:22:58] totally

Paul B (Tutor)

[00:23:05] oh sorry

[00:23:09] URL > http://www.intmath.com/counting-probability/12-binomial-probability-distributions.php

Scott (Customer)

[00:23:13] ok

Paul B (Tutor)

[00:23:38] what page are you on

[00:23:44] what item

[00:23:49] i'm on item 3

Scott (Customer)

[00:24:07] 12. the binomial probability
distribution

Paul B (Tutor)

[00:24:17] cool that's it

[00:24:27] do you see the part called P(X)

Scott (Customer)

[00:24:32] yes

Paul B (Tutor)

[00:25:00] this is the formula that you use to calculate the probability of having x successes out of n trials

Scott (Customer)

[00:25:22] and this is the formula you
just used, correct?

Paul B (Tutor)

[00:25:29] Yes

Scott (Customer)

[00:26:09] Is there any way to plug that
problem into exel and have
excel do the math for you?

Paul B (Tutor)

[00:26:30] yes, but its faster using a calculator, do you have one

Scott (Customer)

[00:26:35] yes

Paul B (Tutor)

[00:26:41] what kind do you have

Scott (Customer)

[00:26:58] ha. i am using the one on my
ipad

Paul B (Tutor)

[00:27:20] what about a texas intrusment calculator

Scott (Customer)

[00:27:38] do I need to get one for this
stats class?

Paul B (Tutor)

[00:28:02] that depends on your teacher, in my class it is mandatory

Scott (Customer)

[00:28:43] i'll see him this weekend and
ask him what he suggest. I'm
active-duty military taking a
Executive MBA course from
UNC

Paul B (Tutor)

[00:29:50] ok, there are many binomials pdf calculators on the internet.
you type in the probability, the number of trials and how many times you want to be successful

Scott (Customer)

[00:30:12] i'll google it

Paul B (Tutor)

[00:30:51] study up on the binomial distribution.
read a few articles on it, this problem is a classic one on the binomial distribution

Scott (Customer)

[00:31:24] i'll do just that. This is my
first weekend with stats so I
need to get smart quick

Paul B (Tutor)

[00:31:41] yes sir, anything else?

Scott (Customer)

[00:31:52] no, thanks for all your help
and patience.

Paul B (Tutor)

[00:32:11] ok, very good, good bye.