Probability Questions

[simplyome]

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So I haven't taken a stats class since first year so I am a little fuzzy on permutations/combinations/probability so can someone give me a little refresher?? (I was stupid and sold all my textbooks and hence have no reference text)

Here is a sample questions that I can't seem to understand if someone can give me a quick on how to set it up? These are from Achiever test 1.

What is the likelihood to have only 1 boy for a family planning to have 3 children??

1/3 cars driven by residents in a town are Japanese made, what is the probability that at least one Japanese car out of 3 cars are on the road?

What is the probability of getting 3 heads and 2 tails with 5 tosses of a coin?

 

[z3u2]

What is the likelihood to have only 1 boy for a family planning to have 3 children??
(3 choose 1) * (0.5)^1 * (0.5)^ 2

1/3 cars driven by residents in a town are Japanese made, what is the probability that at least one Japanese car out of 3 cars are on the road?
1 - (2/3)^3

What is the probability of getting 3 heads and 2 tails with 5 tosses of a coin?
(5 choose 3) * (0.5)^3 * (0.5) ^2

 

[sacjumpman]

What is the likelihood to have only 1 boy for a family planning to have 3 children??
(3 choose 1) * (0.5)^1 * (0.5)^ 2

1/3 cars driven by residents in a town are Japanese made, what is the probability that at least one Japanese car out of 3 cars are on the road?
1 - (2/3)^3

What is the probability of getting 3 heads and 2 tails with 5 tosses of a coin?
(5 choose 3) * (0.5)^3 * (0.5) ^2

what does 3 choose 1 mean?

 

[z3u2]

what does 3 choose 1 mean?

it's binomial coefficient

it determines how many non-ordered combinations exist
http://en.wikipedia.org/wiki/Binomial_coefficient

n choose m
means if there's n choices, and you want to choose m items out of n, where order doesn't matter
n choose m is the number of combinations there is
(n choose m) = n! / ((m!) (n-m)!)

 

[sacjumpman]

it's binomial coefficient

it determines how many non-ordered combinations exist
http://en.wikipedia.org/wiki/Binomial_coefficient

n choose m
means if there's n choices, and you want to choose m items out of n, where order doesn't matter
n choose m is the number of combinations there is
(n choose m) = n! / ((m!) (n-m)!)

ahh... like a combination. I see. That makes sense. It sucks that I knew how to do this problem, this is all stuff I seen before but couldn't put it together... 🙄 Must practice more I suppose.

Thanks for the explanation.

 

[Ocean5]

What is the likelihood to have only 1 boy for a family planning to have 3 children??
(3 choose 1) * (0.5)^1 * (0.5)^ 2

1/3 cars driven by residents in a town are Japanese made, what is the probability that at least one Japanese car out of 3 cars are on the road?
1 - (2/3)^3

What is the probability of getting 3 heads and 2 tails with 5 tosses of a coin?
(5 choose 3) * (0.5)^3 * (0.5) ^2

Could you please explain these more. I don't understabd when you are saying 5 choose 3. Do you mean 5!/ (5-3)! but if that is what you meant, it doesn't seem to be correct in case of this question. I never had achiever, it seems to be really difficult. DO you think should I buy it?

 

[Streetwolf]

5!/(5-3)!3!

Google is your friend everyone!

 

[simplyome]

I was more curious as to how to set up the question not just the numbers. Like how do you know what power to put the probability of p to??

 

[Ocean5]

I was more curious as to how to set up the question not just the numbers. Like how do you know what power to put the probability of p to??

ya me too could some one clearify that please?

 

[z3u2]

general equation:

probability of choosing m items from n choices

(n choose m) * (probability of m)^m * (1- probability of m)^(n - m)

u should try to understand as follows:
(n choose m) = total number of combinations

(probability of m)^m * (1- probability of m)^(n - m) = probabilty for just one of the combination

total probability = (total number of combinations) X (probabilty for just one of the combination)