q_a 6

course Mth 152

I think I understood this section much better. Could you please provide some feedback on how I am doing? Or send me a reminder on how to check myself?

㼯izUw[_Ȋjqyassignment #006

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cʓ齯̀q}li

Liberal Arts Mathematics II

10-11-2006

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19:00:08

Query 12.1.6 8 girls 5 boys

What is the probability that the first chosen is a girl?

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RESPONSE -->

13 people all together, 8 girls

8/13=0.62

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19:00:23

** Assuming the choice is completely random there are 13 possible choices, 8 of which are female so we have

P(female) = 8 / 13 = .6154, approx. **

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RESPONSE -->

ok, I understand. I just rounded up

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19:05:30

Query 12.1.12 3 fair coins: Probability and odds of 3 Heads.

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RESPONSE -->

1/2 for each coin= 0.50

3/1=1/1 are the odds

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19:06:26

** There are 8 equally likely possible outcomes when flipping 3 fair coins. You can list them: hhh, hht, hth, htt, thh, tht, tth, ttt. Or you can use the fact that there are 2 possibilities on each flip, therefore 2*2*2 = 2^3 = 8 possible outcomes.

Only one of these outcomes, hhh, consists of 3 heads.

The probability is therefore

P(3 heads) = # of outcomes favorable/total number of possible outcomes = 1 / 8.

The odds in favor of three heads are

Odds ( 3 heads ) = # favorable to # unfavorable = 1 to 7. **

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RESPONSE -->

ok

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19:12:14

Query 12.1.20 P(pink) from two pink parents (Rr and Rr)

What is the probability of a pink offspring.

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RESPONSE -->

If both parents are Pink, there should be a 100% chance of a pink offspring. However, Do the parents not still possess the red and white passed from their parents? If so, that is still s recessive trait and the chance is lowered to 25% to 75% depending on how you look at it.

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19:12:39

** The genes R and r stand for the red and white genes.

A pink offspring is either Rr or rR. RR will be red, rr white.

R r

R RR Rr

r rR rr

shows that {RR, Rr, rR, rr} is the set of equally likely outcomes. We season two of the four possible outcomes, rR and Rr, will be pink.

So the probability of pink offspring is 2/4 = 1 / 2. **

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RESPONSE -->

Ok, you are going by dominence. I understand

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19:15:42

Query 12.1.33 cystic fibrosis in 1 of 2K cauc, 1 in 250k noncauc

What is the empirical probability, to 6 places, that a randomly chosen non-Caucasian newborn will have cystic fibrosis?

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RESPONSE -->

1/500=0.002 because this is based on the information given in problem 33.

For CF, it is 0.000004

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19:15:48

** There is 1 chance in 250,000 so the probability is 1 / 250,000 = 4 * 10^-6, or .000004. **

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RESPONSE -->

ok

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19:18:07

12.1.40 Cc genes carrier, cc has disease; 2 carriers first child has disease **** What is the probability that the first child has the disease?

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RESPONSE -->

If you write this out in table form, 1/4=0.25. This is the value for cc. There is also a cC so wouldn't they have it in some form as well, making it 0.50?

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19:18:37

** If cc has the disease, then the probability that the first child will have the disease is 1/4. **

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RESPONSE -->

ok, I see, it is only the obvious and I shouldn't look further.

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19:19:34

What is the sample space for this problem?

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RESPONSE -->

I'm not sure what you are asking

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19:20:43

** The sample space is {CC, Cc. cC, cc}. **

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RESPONSE -->

oh, ok, that is what I meant by the table. Mine was the same and is below.

C c

C CC Cc

c cC cc

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19:21:42

12.1.60 36 in class, 3 chosen **** What is the probability that the choice will be the given three people in any order?

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RESPONSE -->

3/36=0.083

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19:22:04

** There are P(36,3) possible ordered choices of 3 people out of the 36.

P(36,3) = 36! / (36-3)! = 36! / 33! = (36*35*34*33*32*31*...*1) / (33*32*31*...*1) = 36*35*34=40,000 or so.

The probability of any given choice is therefore 1 / P(36,3) = 1/40,000 = .000025, approx..

For any given set of three people there are six possible orders in which they can be chosen. So the probability of the three given people, in any order, is 6 * probability of a given order = 6 / P(36,3) = 6/40,000 = .00015.

Alternatively we can say that we are choosing 3 of 36 people without regard for order, so there are C(36,3) possibilities and the probability of any one of them is 1 / C(36,3). **

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RESPONSE -->

ok

This one could use a detailed self-critique.

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19:26:02

Query 12.1.75 digits 1, 2, ..., 5 rand arranged; prob even, prob digits 1 and 5 even What is the probability that the resulting number is even and how did you obtain your answer?

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RESPONSE -->

2 and 4 are the even numbers in this problem

1+2+3+4+5=15

15/75=0.2

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19:26:40

** The number will be even if it ends in 2 or 4. There are 5 possible ending numbers. So 2 of the 5 possible ending numbers are even and the probability of an even number is 2/5.

We analyze in two ways the number of ways to choose a number with digits 1 and 5 even.

First way:

There are 5! = 120 possible arrangements of the 5 digits.

There are only two possible even digits, from which we will choose digit 1 and digit 5. The order of our choice certainly matters, since a different choice will give us a different 5-digit number. So we are choosing 2 digits from a set of 2 digits, where order matters. We therefore have P(2, 2) = 2*1 / 0! = 2 ways to choose these digits.

The remaining 3 digits will comprise digits 2, 3 and 4. We are therefore choosing 3 digits from a set of 3, in order. There are P(3, 3) = 3*2*1/0! = 6 ways to do so.

To obtain our number we can choose digits 1 and 5, then digits 2, 3 and 4. There are P(2, 2) * P(3, 3) = 2 * 6 = 12 ways to do this.

So the probability that digits 1 and 5 are even is 12 / 120 = 1/10.

Second way:

A simpler solution looks at just the possibilities for digits 1 and 5. There are P(2, 2) = 2 choices for which these digits are even, and P(5, 2) = 20 total choices for these two digits. The probability that both will be even is therefore 2/20 = 1/10, the same as before. **

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RESPONSE -->

ok

This one could also use self-critique.

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You did well on most of these problems, but the last couple should have been self-critiqued. You are welcome to copy those problems from this documents and insert self-critiques, and I will of course then be able to give you additional feedback.