by Tutor.com

Tweet
!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';
if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';
fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');

System Message

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

Zebedee (Customer)

[00:00:00] 5.
A student is taking a standardized test consisting several multiple-choice questions.
One point is awarded for each correct answer.
Questions left blank neither receive nor lose points.
If there are six options for each question and the student is penalized 1/3 point for each wrong answer, how many options must the student be able to rule out before the expeced value of guessing zero?
The number of options the student must be able to rule out before the expected value of guessing becomes zero is _____

Kevin P (Tutor)

[00:00:08] Welcome to Tutor.com .
My name is Kevin.
How are you doing today?

Zebedee (Customer)

[00:00:14] lost

Kevin P (Tutor)

[00:00:28] I'm sorry to hear that.

Zebedee (Customer)

[00:00:28] math is so difficult

Kevin P (Tutor)

[00:00:40] I'll do my best to help you.

Zebedee (Customer)

[00:00:45] thank you

Kevin P (Tutor)

[00:00:46] Let's see what we have in this problem.

Zebedee (Customer)

[00:00:52] ok

Kevin P (Tutor)

[00:01:32] ok.
We are talking abut expected value.

Zebedee (Customer)

[00:01:39] right

Kevin P (Tutor)

[00:01:50] Give me one second to make sure my thoughts are correct.

Zebedee (Customer)

[00:02:04] okay

Kevin P (Tutor)

[00:03:13] ok.
Do you know how we calculate expected value?

Zebedee (Customer)

[00:03:22] no i'm dumb

Kevin P (Tutor)

[00:03:39] No your not.

Zebedee (Customer)

[00:03:47] E=something

Kevin P (Tutor)

[00:03:53] True

[00:03:59] How many choices do we have?

[00:04:05] for the question

Zebedee (Customer)

[00:04:05] six

Kevin P (Tutor)

[00:04:08] Correct

[00:04:19] Write them on the board as choices A to F

[00:04:58] Good job.

Zebedee (Customer)

[00:05:03] thank you

Kevin P (Tutor)

[00:05:08] Which one do you want to make the correct answer?

Zebedee (Customer)

[00:05:22] c

Kevin P (Tutor)

[00:05:26] Sounds good.

[00:06:45] Now we need two things . . .

Zebedee (Customer)

[00:06:55] +6/6+x5/5 something like that

Kevin P (Tutor)

[00:07:16] ok.
Keep that thought in mind

Zebedee (Customer)

[00:07:21] okay

Kevin P (Tutor)

[00:07:44] We need the total points earned or loss for picking each choice

[00:07:52] and the probability of guessing each choice.

Zebedee (Customer)

[00:07:59] 1/3 point

Kevin P (Tutor)

[00:08:06] Gain or loss?

Zebedee (Customer)

[00:08:31] 1/3 for each wrong answer

Kevin P (Tutor)

[00:08:42] and which letters are the wrong answers?

Zebedee (Customer)

[00:08:42] one point for each correct
answer

[00:08:51] a,b,d,e,f

Kevin P (Tutor)

[00:08:55] Correct!

[00:09:10] Write -1/3 in the points column of each wrong answer.

[00:09:57] Don't forget the negatives

[00:10:16] Good

[00:10:28] How many points do we earn if we choose C?

Zebedee (Customer)

[00:10:38] one

Kevin P (Tutor)

[00:10:45] Write that in.

[00:11:07] Now . . . what is the probability of picking one of these six choices at random?

Zebedee (Customer)

[00:11:35] 1/6

Kevin P (Tutor)

[00:11:39] Excellent!

[00:11:47] Write that in the probability column

[00:12:21] 1/6

[00:13:12] Actually, they are positive.

[00:13:22] There's no such thing as negative probability

Zebedee (Customer)

[00:13:33] okay

Kevin P (Tutor)

[00:13:44] Now we are ready to calculate expected probability.

[00:14:01] What do we do with each row of numbers?

[00:14:53] That's a good check

[00:15:13] How do we calculate the expected value of choice a?

[00:15:44] What symbol is that?

Zebedee (Customer)

[00:15:51] multiplication

Kevin P (Tutor)

[00:15:50] You got it!

[00:16:01] That's correct!

[00:16:08] Multiply across all six columns

[00:16:41] keep it as a fraction . . . -1/18

[00:16:55] Continue

[00:18:46] Very good!

[00:18:51] and the last step is . . .

Zebedee (Customer)

[00:19:20] adding

Kevin P (Tutor)

[00:19:27] Go for it!

[00:21:10] Almost.

[00:21:15] I agree with the -5

[00:21:31] Adding all of those -1/18 gives you -5/18

[00:21:47] Even closer!!!!

[00:22:13] I get -2/18

Zebedee (Customer)

[00:22:29] reduce it?

Kevin P (Tutor)

[00:22:46] Not necessary because we are looking for 0

Zebedee (Customer)

[00:22:56] so negative 2/18

Kevin P (Tutor)

[00:23:00] Correct

[00:23:16] Now . . . let's see what happens when we cross out a choice.

Zebedee (Customer)

[00:23:28] okay

Kevin P (Tutor)

[00:23:31] Which wrong answer do you want to eliminate?

Zebedee (Customer)

[00:23:38] f

Kevin P (Tutor)

[00:23:40] ok

[00:23:44] So now we have this . . .

[00:24:06] Any changes in the points for each choice?

Zebedee (Customer)

[00:24:26] no one is still correct

Kevin P (Tutor)

[00:24:32] That's right

[00:24:51] but . . .

[00:25:12] What's the probability of each choice?

Zebedee (Customer)

[00:25:27] 1/5

Kevin P (Tutor)

[00:25:31] Excellent!!!

[00:25:45] Write that down and calculate the expected value.

[00:26:13] Do you feel you can continue this problem on your own or would you like to finish with me?

Zebedee (Customer)

[00:26:27] I can continue it

Kevin P (Tutor)

[00:26:32] Sounds great.

Zebedee (Customer)

[00:26:35] thank you for your help

Kevin P (Tutor)

[00:26:40] Keep going until you find 0.

[00:26:43] My pleasure.

[00:26:51] Thank you for using Tutor.com .

[00:26:55] Could you do me a favor and please fill out the survey at the end of the session?

Zebedee (Customer)

[00:27:01] but the answer is -2/18 right

Kevin P (Tutor)

[00:27:10] For the first one.

[00:27:26] You are looking for the number of choices you removed to get an expected value of 0.

[00:27:35] the -2/18 needs to turn into a 0.

[00:27:57] Good luck!
Have a great night!

Zebedee (Customer)

[00:28:00] I m lost

Kevin P (Tutor)

[00:28:10] ok.
Keep going with the current problem.

[00:28:17] Fill in the 1/5 and multiply across.

Zebedee (Customer)

[00:29:53] right

Kevin P (Tutor)

[00:30:05] so far . . . what does the 1/5 turn into?

[00:30:42] 5 times what is 15?

[00:30:55] There you go!!!

[00:31:03] Which equals . . .

[00:31:12] Good

[00:31:21] We're closer to 0 but not quite there.

[00:31:33] let's eliminate one more wrong choice.

[00:31:58] Which letter?

Zebedee (Customer)

[00:32:20] e

Kevin P (Tutor)

[00:32:38] Give it a try.

[00:33:57] Careful . . . how many choices do we have?

Zebedee (Customer)

[00:34:07] 4

Kevin P (Tutor)

[00:34:10] Right!

[00:34:24] Change the 6's to 4's.

[00:35:01] Good.
Continue

[00:35:11] Multiply across

[00:35:39] Multiply first . . .

[00:35:56] then add

Zebedee (Customer)

[00:36:21] lost

Kevin P (Tutor)

[00:36:29] 1 times 1/4

[00:36:44] and now a and b

[00:37:00] that one is 3 times 4

[00:37:08] same as d

[00:37:27] 3 times 4 is what?

Zebedee (Customer)

[00:38:01] no

Kevin P (Tutor)

[00:38:13] Those are -1/12 as well

[00:38:18] 1/3 times 1/4

[00:38:35] Actually, the C stays 1/4

[00:38:42] C gains 1 point

[00:38:47] not losing 1/3

[00:38:54] Right!

[00:39:07] Now we finish by adding this column

Zebedee (Customer)

[00:39:22] 4 not a common denominator

Kevin P (Tutor)

[00:39:34] true, so we change 1/4 to a denominator of 12

[00:39:41] What goes in the numerator?

Zebedee (Customer)

[00:39:48] -1

Kevin P (Tutor)

[00:39:55] 1 times 3 is . . .

[00:40:30] Whoops.
That's supposed to be times 3

[00:40:35] My mouse slipped

Zebedee (Customer)

[00:40:41] okay

Kevin P (Tutor)

[00:40:56] Good

[00:41:03] How many -1's do we have?

Zebedee (Customer)

[00:41:12] 3

Kevin P (Tutor)

[00:41:21] and a positive 3 . . .

[00:41:31] so our expected value is . . .

[00:41:35] YEAH!!!!

[00:41:39] We have 0

[00:41:52] How many answers did we eliminate to get here?

Zebedee (Customer)

[00:42:07] what do i put for the answer a
zero or the
we eleimated 3

[00:42:12] eliminated

Kevin P (Tutor)

[00:42:24] the number of choices we removed.

[00:42:28] Which was how many?

Zebedee (Customer)

[00:42:33] 3

Kevin P (Tutor)

[00:42:41] We started with 6

[00:42:49] we currently have 4

Zebedee (Customer)

[00:42:49] f,e

[00:42:54] two

Kevin P (Tutor)

[00:42:58] Right!!!

[00:43:06] Thank you for your hard work.

Zebedee (Customer)

[00:43:31] your hard work so the answer
is -2/18 and two

Kevin P (Tutor)

[00:43:41] Just the two

Zebedee (Customer)

[00:43:50] just the two for the final
answer

Kevin P (Tutor)

[00:43:56] Correct

[00:44:04] have a great night!

Zebedee (Customer)

[00:44:08] okay I am on the last problem
I will log back in

Kevin P (Tutor)

[00:44:14] Sounds good.

Zebedee (Customer)

[00:44:15] you as well you are great