Math Is Fun Forum

jubadedo

Member

Registered: 2015-04-05

Posts: 19

Probability Help

Hi guys,
I hope everyone's been well.

Could someone explain how they figure out these 4 problems? I would truly appreciate it.

1. How many ways are there to choose one-half dozen donuts from 9 varieties so that there are exactly 4 glazed?

2. How many distinct ways are there for arranging the letters in “arranging” so that the vowels are together in 
any order?

3. A box of 10 RAM chips contains three defective and seven good chips. Three chips are chosen at random without replacement from this box and tested. What is the probability that exactly one of the chips is defective?

4. On a given day, there is a 0.7 probability that it is sunny. Jane walks past an ice cream stand every day. When it is sunny, the probability that she buys an ice cream is 0.8. When it isn't sunny, the probability that she buys an ice cream is 0.1.
What is the probability that Jane buys an ice cream?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability Help

How many are glazed?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

jubadedo

Member

Registered: 2015-04-05

Posts: 19

Re: Probability Help

Hi Bobbym,

Okay I think I've made progress

1. Okay we have six donuts

4 of them have already been decided, so we need to pick 2. So there are 9 flavors to choose from and order doesn't matter and I think there's no replacement? Either way, it's C(2+9-1,2) = C(10,2) = 45.

2. I have three vowels that I can place vowels in 7 different ways, then I can have 6! constant order and 3! vowel  after that, so that's 7 x 6! x 3! = 30240

3. I forget how to do it but I have an idea I think...

4. I have no idea :*(

Last edited by jubadedo (2016-02-08 16:01:45)

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Probability Help

Hello!

3. The probability is:

You get 7/40 from multiplying the chance of each step in any sequence that leads to one bad chip (e.g. 7/10*6/9*3/8 for the third chip being bad or 3/10*7/9*6/8 for the first). Then multiply 7/40 by three since there are three ways to do this (first chip, second chip, or third chip is bad).

4. You need to multiply the conditional probabilities together. When she buys an ice cream 80% of 70% of the time, you multiply those two together. So we get:

Last edited by Relentless (2016-02-08 15:57:48)

jubadedo

Member

Registered: 2015-04-05

Posts: 19

Re: Probability Help

Thank you so much Relentless

I appreciate the help a lot!!!!!

Last edited by jubadedo (2016-02-08 16:01:01)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability Help

For 1) I still need more info, What do you mean by glazed.

For 2) I am getting 1890.

For 3) you can use the hypergeometric distribution which is designed for this type problem. The answer is 21 / 40.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Probability Help

Hello again!

For 2. Bobbym is correct. The mistake you made was to keep track of every single letter when in fact there are a lot of duplicates. In fact, there are four pairs of matching letters, and 2^4 = 16, so you counted each arrangement 16 times. This is why, when you divide your answer by bobbym's, you get 16.
Your method would work if every letter is different, but when there are identical letters you have to divide by the number of identical arrangements..

Last edited by Relentless (2016-02-09 01:31:27)