Query 9

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course Mth 152

7/01 10:49pm

If your solution to stated problem does not match the given solution, you should self-critique per instructions athttp://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.

009. ``q Query 9

`q Query 12.4.3 P(2 H on 3 flips)

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Your solution:

hhh, hht, hth, htt, thh, tht, tth, ttt, There are 8 possibilities and three of them have two heads. So probability would be 3/8.

confidence rating #$&*: 3

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Given Solution:

On three flips you can get HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

• Of these 8 possibilities, only 3 of them have two Heads.

• Thus the probability is 3 / 8.

You can get this result without listing.

• There are 2 possibilities for each flip which gives you 2*2*2 = 2^3 = 8 possible outcomes.

• To get 2 `heads' you must get `heads' in exactly 2 of the 3 positions.

• There are C(3, 2) = 3 possible choices of the 3 positions so the probability is C(3,2) / 2^3 = 3/8.

More generally, if you have n flips, there are C(n,r) ways to get r Heads. The value of C(n, r) appears in the n+1 row, as the r+1 entry, of Pascal's triangle.

STUDENT COMMENT:

I solved this question using the given solution for binomials, it might have been more work, but I’m guessing it’s ok?

INSTRUCTOR RESPONSE:

Your solution is fine. Make sure you also understand the given solution, which is a reasoning process as opposed to a formula. From your previous work I'm confident you do.

Knowing how the formula represents the reasoning process, you can then use the formula with confidence.

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Self-critique (if necessary):

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Self-critique Rating: 3

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Question: What is the significance of .5^2 * .5 for this question?

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Your solution:

.5^2 is probability for getting heads two times in row.

Then .5 would be probability of tails.

So if you have C(3,2) possible orders then C(3,2)*.5^2*.5=3*.125=.375

confidence rating #$&*: 2

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Given Solution:

.5^2 is the probability of getting Heads twice in a row.

.5 is the probability of a Tails.

• .5^2 * .5 is therefore the probability of getting HHT.

Since the probabilities are independent, you have the same probability of getting two Heads and a Tail in some different order.

Since there are C(3,2) possible orders for 2 Heads on 3 coins, the probability of getting 2 Heads and one Tail is

• C(3,2) * .5^2 * .5 = 3 * .125 = .375,

the same as the 3/8 we obtained by listing.

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Self-critique (if necessary):

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Self-critique Rating: 3

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Question: `q Query 12.4.6 P(>= 1 H on 3 flips) Give the requested probability and explain how you obtained your result.

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Your solution:

If you have 3 flips and the probability is no heads and one is P(TTT)= .5*.5*.5=.125

So you would have 1/8 getting tails and you subtract from 1 then you

Would have 7/8 of chance.

confidence rating #$&*: 2

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Given Solution:

Probability of getting no heads on three flips is P(TTT) = .5 * .5 * .5 = .125, or 1/8, obtained by multiplying the probability of getting a tails for each of 3 independent flips.

Subtracting this from 1 gives .875, or 7/8.

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Self-critique (if necessary):

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Self-critique Rating: 3

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Self-critique (if necessary):

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Self-critique Rating:

Query 12.4.15 P(3 H on 7 flips) Give the requested probability and explain how you obtained your result.

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Your solution:

If you have C(7,3) = 7*6*5/3!=35 ways for 3 heads on 7 flips. The probability of 3 heads on 7 flips would be 35* 1/128=35/128.

confidence rating #$&*: 2

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Given Solution:

There are C(7,3) = 7 * 6 * 5 / 3! = 35 ways to choose three of the 7 `positions' for Heads on 7 flips. So there are C(7,3) = 7 * 6 * 5 / 3! = 35 ways to get three heads on 7 flips.

The probability of any of these ways is (1/2)^3 * (1/2)^4 = 1 / 2^7 = 1 / 128.

The probability of 3 Heads on 7 flips is therefore 35 * 1/128 = 35 / 128. **

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Self-critique (if necessary):

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Self-critique Rating: 3

&#This looks good. Let me know if you have any questions. &#