Interpreting probability


by musicgold
Tags: interpreting, probability
musicgold
musicgold is offline
#1
Jan23-12, 08:48 PM
P: 178
Hi,

My question is related to the following problem.

80% of all California drivers wear seat belts. If three drivers are pulled over, what is the probability that all would be wearing their seat belts?

Now I know that the answer of this problem is = 0.8 * 0.8 * 0.8 =
(Probability of the first person wearing belt x prob. of the second person wearing belt x)

However, there is another question that comes to my mind. What if we say that 80% of the sample (of the three people) will be wearing seat belts? Or do we have to always treat them as Bernoulli trials?

Thanks.
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SW VandeCarr
SW VandeCarr is offline
#2
Jan23-12, 09:27 PM
P: 2,490
Quote Quote by musicgold View Post
Hi,

My question is related to the following problem.

“80% of all California drivers wear seat belts. If three drivers are pulled over, what is the probability that all would be wearing their seat belts?”

Now I know that the answer of this problem is = 0.8 * 0.8 * 0.8 =
(Probability of the first person wearing belt x prob. of the second person wearing belt x…)

However, there is another question that comes to my mind. What if we say that 80% of the sample (of the three people) will be wearing seat belts? Or do we have to always treat them as Bernoulli trials?

Thanks.
The short answer is yes. As you take larger and larger samples the expectation is that the sample distributions would approach P(B)=0.8; P(~B)=(1-P(B))=0.2

However the probability that all individuals in the sample were wearing seat belts would approach [itex]P=(0.8)^n[/itex] where n is the sample size.

For a sample of size 3, there will be considerable variability with 2 or 3 being more likely than 0 or 1 wearing seat belts. Do you know how to calculate the exact probabilities of 0,1 or 2 drivers wearing seat belts (assuming P(B) holds for the population)?
musicgold
musicgold is offline
#3
Jan25-12, 12:37 PM
P: 178
SW VandeCarr,

Thanks.

Yes, I do know how to calculate the probabilities of 0,1 or 2 drivers wearing seat belts.

SW VandeCarr
SW VandeCarr is offline
#4
Jan25-12, 02:15 PM
P: 2,490

Interpreting probability


Quote Quote by musicgold View Post
SW VandeCarr,

Thanks.

Yes, I do know how to calculate the probabilities of 0,1 or 2 drivers wearing seat belts.
You're welcome.


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