Open Query 11

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course mth 152

10/29 1:20I could not open the QA 11 assignment. I tried several times.

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution.

If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

011.

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question: Query 11

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Question: Query 12.6.6 rnd # table to simulate 50 one-and-one foul shooting opportunities if 70% prob of success; 2 shots

Give the results of your tally.

How does your empirical probability compare with the theoretical probability?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

theoretical probability is stated:

0 points=.30

1 point=.21

2 ponts=.49

if 70% of her shots are made then 30% are missed.

If you miss the first shot you do not get a second= 0 points=.30

If you make the first=.70, but miss the second=.30 then .70*.30=.21

If you make the first=.70, then make the second=.70 then .70*.70=.49

.30+.21+.49=1 shows that each is a possibility

1-7=make

8,9,0=miss

hh hh m hm m hh hh m m hh hh m hh hh hh

hh hm hh hh hh hh hh hh hh hh m hh m hh

m hh m m m hm hh m m hm m hh hh hm m m hm

m hh m hm

m=0 points 18/50 times=.36

hm=1 point 7/50 times=.14

hh=2 points 25/50 times=.50

.50+.14+.36=1

confidence rating #$&*:

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Given Solution:

`aIn 1-and-1 shooting you only get a second shot if you make the first. So there are 3 possibilities:

miss the first, don't get another shot

make the first, get another shot and make it

make the first, get another shot and miss it

prob of 0 = prob of miss on first shot = .3

prob of 1 = prob of hit on first and miss on 2d = .3 * .7 = .21

prob of 2 = prob ot hit * prob of hit = .49.

'Hits' happen with 70% or .7 probability, misses with probability 30% or 3.

The theoretical probability of missing the first shot (and therefore not getting another shot, thereby scoring 0) is just

probability of miss = .30

The theoretical probability of 1 miss and 1 hit is

probability of hit * probability of miss = .7 * .3 = .21

The theoretical probability of 2 hits is

probability of hit * probability of hit = .70 * .70 = .49.

Note that these probabilities add up to .30 + .21 + .49 = 1, as they must since these three events cover all possibilities.

To use the table, randomly pick a starting point. Let numbers 1-7 correspond to making the free throw, with 8, 9 and 0 corresponding to misses. Go down the list, or across the list in an order you decided before looking at the list.

Read two digits from the list and see if they correspond to two 'hits', two 'misses' or a 'hit' and a 'miss'. Record your result as 'hit-miss', 'miss-hit', 'miss-miss' and 'hit-hit'.

Read two more digits and record your result as 'hit-miss', 'miss-hit', 'miss-miss' and 'hit-hit'.

Continue until you have the required number of results.

Tally how many times you got 0 'hits', 1 'hit', 2 'hits' etc..

Any outcome that starts with a 'miss' corresponds to zero point. 'Hit-miss' corresopnds to

1 point and 'hit-hit' corresponds to 2 points.

Determine the percent of time you got each number of points, and compare to the theoretical probabilities .30, .21 and .49. *&*& **

Self-critique

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Self-critique Rating:

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question: Query 12.6.12 rnd walk start N then right, left or straight with prob 1/2, 1/6, 1/3; 1 st 2 columns of table

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

right-1,2,3

left-4

straigt-5,6

no change-7,8,9,0

right probability=1/2 or 3/6=.50

left probability=1/6=.16

straight=1/3 or 2/6=.33

R R R S S S S L R L S R R R S S R R R S S S S

RIGHT=9/23=.391

LEFT=2/23=.086

SRAIGHTS=12/23=.521

.391+.086+.521=.998

confidence rating #$&*:

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Given Solution:

`aYour probabilities are given as 1/2, 1/6 and 1/3. These can all be expressed in terms of the common denominator 6:

1/2 = 3/6, 1/6 = 1/6, 1/3 = 2/6.

So a move to the right has 3 chances out of 6, a move to the left has 1 chance out of 6 and a move straight has 2 chances out of 6.

You can simulate this by letting the three digits 1, 2, 3 stand for a move to the right, the single digit 4 for a move to the left and the two digits 5, 6 for a straight move. The remaining digits 0, 7, 8, 9 don't stand for anything, and if you land on one of these numbers you just move to the next number.

So according to your the first two columns of you table, how many times do you move to the right, how many to the left, how many straight and where do you end up? **

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Self-critique (if necessary):

Having to look back and forth and back and forth between the book, the computer screen and the keyboard has the numbers jumbled not only on the screen here but in my head as well.

I do not know if I understand this now or not. this sounds silly, but I got my lefts, rights and straights and the numbers assigned to them, that I'm lost. I originally had assigned

right to have 4,5,6 with left having 1 and straight having 2,3. Because of the numbers given on the table in the book, I came up with totally different results. I put an hour into this problem

alone. That's way too long to still be confused!

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Self-critique Rating:

@&

You would have done this problem in the book when you did the assignment, and that would have involved the book, paper and pencil with no computer screen.

In any case your results are plausible, but not very likely.

You would have simply gone down the first column of the table and written R if you saw the numbers 1, 2 or 3, L if you saw 4 and S if you saw 5 or 6.

Having done so it is likely you would have see nore 1's, 2's and 3's than 5's or 6's, and it's unlikely that the latter would have occurred 12 times while the former occurred only 9. Still, that is possible.

It sounds as though you might have been moving right, left and straight through the random numbers. That would be more or less valid, but woulld give results different from those you would have obtained by moving down the columns.

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Question: Query Add comments on any surprises or insights you experienced as a result of this assignment.

`Self-critique

Both of these questions required far too much time spent between have to find numbers in a table in the book and TYPING the values onto this page. I am not the best typer and I lost alot of

understanding of the problem some where in between. My suggestion would be to put the ""TABLE"" on the screen. It might help.

@&

Check my note above. I don't recommend that you're on the screen when you solve the text problems.

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However having the table onscreen wouldn't be a bad idea, for mutual reference.

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Self-critique Rating:

&#Good responses. See my notes and let me know if you have questions. &#