probability

sharohaddox

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OK so I have a few problems I've been working on and my textbooks has both the problems and answers, but I can't figure out how they GOT the answers so please if you have a chance, tell me what I am doing wrong. I read Ted's post and I'm going to list three questions. (I hope I am not pushing my luck, but two a reletively similar, sort of.)

My first question number 19) reads "In a civic organization there are 38 members; 15 are men and 23 are women. If 3 members are selected to plan a parade, find the probability that all 3 are women."
So on my paper I did 23/38 x 23/38 x 23/38 which equaled 12167/54872 and my answer was 0.222 (we were told by our teacher we could round to 3 decimal places.) But the answer they are showing in our book is 0.210, so somehow I am .12 off and I can't figure out why.

My second question I am totally lost on is number 23) "An insurance company classifies drivers as low-risk, medium risk, and high risk. Of those insured 60% are low-risk, 30% are medium risk, and 10% are high risk, After a study, the company finds that during a 1-year period, 1% of the low risk drivers had an accident, 5% of the medium risk drivers had an accident and 9% of the high risk drivers had an accident. If a driver is selected at random, find the probablity that the driver will have an accident during the year. "
I would tell you what I did on my paper, but I erased and reworked this problem so many times in so many different way trying to get the correct number, I wouldn't know where to begin. LOL, I think I worked it like 10 times? In ten different ways. I thought surely if I tried trial and error I would figure it out. My paper is so marked up with smeared eraser and graphite smudges it is rediculous on this problem. Oh and their answer is .03 which I have NO idea where that came from.

My last question, (if you have time to answer it) is a different type. I couldn't finnish those two problems and instead of quitting, I temporarily moved onto something else. This one lost me.
9) How many different 3-digit ID tags can be made a)if the digits can be used more than once. b)If the digit must be a 5 and repetitions are not permitted.
a)10x10x10=1000 b)10 x 9 x 8 =720 (since repitions are not permited) but how do I specify that there must be a 5? my answer A is correct it is 1000, but for answer B the book has 72, but there is no formula or anything explaining why.

OK so I hope I didn't overload whoever ends up reading this or ask too many question, but any help or guidance that could be given would be greatly and vastly apprechiated.
Thanks so much again
Sharo.
 
sharohaddox said:
OK so I have a few problems I've been working on and my textbooks has both the problems and answers, but I can't figure out how they GOT the answers so please if you have a chance, tell me what I am doing wrong. I read Ted's post and I'm going to list three questions. (I hope I am not pushing my luck, but two a reletively similar, sort of.)

My first question number 19) reads "In a civic organization there are 38 members; 15 are men and 23 are women. If 3 members are selected to plan a parade, find the probability that all 3 are women."
So on my paper I did 23/38 x 23/38 x 23/38 which equaled 12167/54872 and my answer was 0.222 (we were told by our teacher we could round to 3 decimal places.) But the answer they are showing in our book is 0.210, so somehow I am .12 off and I can't figure out why.

How many ways you can choose 3 women out of a group of 23 women = [sub:24qjucfl]23[/sub:24qjucfl]C[sub:24qjucfl]3[/sub:24qjucfl] = 1771

How many ways you can choose 3 people out of a group of 38 people= [sub:24qjucfl]38[/sub:24qjucfl]C[sub:24qjucfl]3[/sub:24qjucfl] = 8436

Probability of choosing 3 women committee out of a group with 23 women and 15 men = 1771/8436 = 0.209933618 = 0.210


My second question I am totally lost on is number 23) "An insurance company classifies drivers as low-risk, medium risk, and high risk. Of those insured 60% are low-risk, 30% are medium risk, and 10% are high risk, After a study, the company finds that during a 1-year period, 1% of the low risk drivers had an accident, 5% of the medium risk drivers had an accident and 9% of the high risk drivers had an accident. If a driver is selected at random, find the probablity that the driver will have an accident during the year. "

The chance of choosing a driver from low-risk = x
Chance of low-risk driver having an accident = y

Chance of choosing a low-risk driver and her having an accident = x * y ...................................(1)

The chance of choosing a driver from medium-risk = u
Chance of low-risk driver having an accident = v

Chance of choosing a medium-risk driver and him having an accident = u * v...................................(2)

The chance of choosing a driver from high-risk = p
Chance of low-risk driver having an accident = q

Chance of choosing a high-risk driver and her having an accident = p * q...................................(3)

Calculate (1), (2) & (3) and add those up to get total probability



I would tell you what I did on my paper, but I erased and reworked this problem so many times in so many different way trying to get the correct number, I wouldn't know where to begin. LOL, I think I worked it like 10 times? In ten different ways. I thought surely if I tried trial and error I would figure it out. My paper is so marked up with smeared eraser and graphite smudges it is rediculous on this problem. Oh and their answer is .03 which I have NO idea where that came from.

My last question, (if you have time to answer it) is a different type. I couldn't finnish those two problems and instead of quitting, I temporarily moved onto something else. This one lost me.
9) How many different 3-digit ID tags can be made a)if the digits can be used more than once. b)If the digit must be a 5 and repetitions are not permitted.
a)10x10x10=1000 b)10 x 9 x 8 =720 (since repitions are not permited) but how do I specify that there must be a 5? my answer A is correct it is 1000, but for answer B the book has 72, but there is no formula or anything explaining why.

Since one digit must be 5 - we are left with 9 digits and 2 spaces to fill...... now continue.

OK so I hope I didn't overload whoever ends up reading this or ask too many question, but any help or guidance that could be given would be greatly and vastly apprechiated.
Thanks so much again
Sharo.
 
Hello, sharohaddox!

19) In a civic organization there are 38 members; 15 are men and 23 are women.
If 3 members are selected to plan a parade, find the probability that all 3 are women.

\(\displaystyle \text{So on my paper I did: }\;\frac{23}{38} \times \frac{23}{38} \times \frac{23}{38}\) . . . . . no

\(\displaystyle \text{You should have had: }\;\frac{23}{38} \times \frac{22}{37} \times \frac{21}{36} \;=\;\frac{1771}{8436}\)

. . which matches Subhotosh's answer.
 
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