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[sspeedy]

Ok, I practiced all the cute probability questions that supposedly cover this stuff and I did halfway ok on those. Now I look at these two practice questions for a test tomorrow and I"m like 'wtf, how'd he get those answers!?'

so please, help me out here and tell me exactly how you got the answers.

According to a survey, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had two cars. The probability that the residents of a household own 2 cars and have an income over $25,000 is:
a) 0.12
b) 0.18
c) 0.22
d) 0.48

A company has two machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. What is the probability that a randomly chosen widget produced by the company is defective?


Thanks in advance.

EDIT: Since you're all so helpful, here's 'nother one:
The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be .74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that both house sales and interest rates will increase during the next six months is:
a)0.10
b) 0.185
c) 0.705
d) 0.90

For the car and income question, that "70% had two cars." really screwed me over.
To be one of you can't take this test for me tomorrow

 

[Vennt]

how would you solve this...

I'd listen hard at school/college/whatever and either know, or ask my teacher/tutor/whoever to explain it to me again if I didn't...

 

[Boomer]

Wouldn't the last problem be.... 8% ?

 

[malek4980]

1st. .8 * .6 = .48, the last number is a red herring, you don't care about general two car ownership since you know the rate of ownership for households over $25 000, which is 80%.





0.1175

How'd I get this answer. Last time I did any math was in grade 9 so...

Hypothetically the older machine makes 100 widgets, thus 23 would be defective.
The newer machine, since it makes 3 times as many makes 300. 8*3 = 24 defective

24 + 23 = 47 47/400 = 0.1175 11.75%

 

[Ecrofirt]

I've never taken a probability class, but I'll take a stab at the second one.

Let's assume Machine A outputs 100 widgets. 23% are defective, so 23 widgets are defective.
Machine B would then output 300 widgets. 8% are defective, so 24 widgets are defective.

That gives us a total of 400 widgets, with 47 defective. that's 11.75% defective widgets.

 

[Johntk5]

1. D

0.80*0.60=0.48

2. 0.1175 or 11.75%

(3/4)(0.08)+(1/4)(0.23) = 0.1175

 

[GhaleonEB]

Wouldn't the last problem be.... 8% ?

No, there's two machines, not just the one.

A company has two machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. What is the probability that a randomly chosen widget produced by the company is defective?

So for ever unit the first produces, the other produces three. The former has a 23% failure rate, the other 8%.

So if you have 100 units produced on the old machine, there would be 23 defective ones, and of 300 units on the new, 24 defective ones. I'd say the answer is just the total produced divided by the total average failures.

(23 + 24)/(100 + 300) = .1175

Then again, I sucked at statistics because I insisted on using algebra and logic, and not these insane general forumals, to solve problems.

*edit* I see in the time I typed that out I was severely beaten. Curses.

 

[Traumahound]

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be .74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that both house sales and interest rates will increase during the next six months is:
a)0.10
b) 0.185
c) 0.705
d) 0.90

b) 0.185

The 0.89 is another red herring. You're trying to find sales (S=0.25) and interest (I=0.74). It doesn't matter what the probability of (S OR I) is, just the probability of (S AND I). So, simply, 0.25 * 0.74 = 0.185.

 

[malek4980]

red herring -- An attempt to divert attention away from the crux of an argument by introduction of anecdote, irrelevant detail, subsidiary facts, tangential references, and the like.

Look out for these on the test, seems like you are having some trouble with irrelevant data.

 

[Johntk5]

b) 0.185

The 0.89 is another red herring. You're trying to find sales (S=0.25) and interest (I=0.74). It doesn't matter what the probability of (S OR I) is, just the probability of (S AND I). So, simply, 0.25 * 0.74 = 0.185.

Nope

The answer is 0.10. All the numbers are needed.

P(A and B ) = P(A) + P(B) - P(A or B) = .25+.74-0.89=0.10

Your formula only works if A and B are independent.

 

[malek4980]

Nope

The answer is 0.10. All the numbers are needed.

P(A and B ) = P(A) + P(B) - P(A or B) = .25+.74-0.89=0.10

Your formula only works if A and B are independent.

I believe you are wrong.

 

[Johntk5]

I believe you are wrong.

I assure you I am not wrong.

P(A and B) = P(A)*P(B) if and only if A and B are independent.

P(A and B)= P(A) + P(B) - P(A or B) is ALWAYS true.

 

[Trident]

I believe you are wrong.

No, he's right. Think of a Venn diagram. Two intersecting circles. The first circle is the probability of A, and the second circle is the probability of B. The intersection is A AND B. The total is A OR B. If you add the probability of A with the probability of B, the intersection is added in twice. So if you subract A OR B, all that's left is the intersection.

 

[sspeedy]

yeah, answer should be .10.

i'm having trouble breaking things down and using the appropriate formulas. any tips on how to keep my head straight with the formulas?