Assignment 11 Query

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course MTH 152

3/13 11

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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?

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Your solution:

There are three possible outcomes for one-and-one foul shooting: [(miss the first shot, do not get another shot), (make the first shot, get another shot and do not make it), and (make the first shot, get a second shot and do make it).] The probability of a hit is 70% or .7, and the probability of a miss is 30% or .3. Therefore, the probability of the first possibility (miss the first shot, do not get another shot) is .3. The probability of the second possibility (make the first shot, get another shot and do not make it) is .3*.7, or .21. The probability of the third possibility (make the first shot, get a second shot and make it) is .49. When I tallied up the random possibilities of hit-hit, miss-, and hit-miss using the given chart, I got 18 miss- possibilities, 8 hit-miss possibilities, and 24 hit-hit possibilities. These results suggest that there is a .36% probability of a miss- result, a .16% probability of a hit-miss result, and a .48% probability of a hit-hit result. Compared to the theoretical probability, our results are not that far off. The biggest difference in probability is the probability of a hit-miss result. Our theoretical probability for this result is .21, and the probability we got from our chart is only .16.

confidence rating #$&*: 3

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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: OK

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Self-critique Rating: OK

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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

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Your solution:

According to the given conditions of the problem (1=left, 2 and 3=straight, and 4, 5, and 6=right) 23 of the numbers in the far left columns were applicable. 4 of the numbers yielded a left turn, 5 of the numbers yielded a straight, and 14 of the numbers yielded a right turn. We end up 23 blocks from where we began, heading right.

confidence rating #$&*: 3

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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): OK

Self-critique Rating: OK

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

`Self-critique: OK

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Self-critique Rating: OK

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&#Good responses. Let me know if you have questions. &#