2 probability questions

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April 10th 2006, 05:15 PM
munkeyb0i

2 probability questions

I have just recently been learning probability and I have been having troubles with some questions. If someone can help me on these two question, I would appreciate it.

1. A basketball player has a success rate of 80% for shooting free throws. What is the probability she will make atleast three out of 5 attempts.

2. A person is chosen at random from shoppers at a store. If the person's probability of having blonde hair and glasses is 2/25 and the probability of wearing glasses is 9/25, determine P(blonde hair|wears glasses).
The only thing I could do is do a venn diagram for this question and I'm not too sure if it's even right. Please reply if you know how to do these two questions.

Thanks
April 21st 2006, 04:06 AM
CaptainBlack

Quote:

Originally Posted by munkeyb0i

1. A basketball player has a success rate of 80% for shooting free throws. What is the probability she will make atleast three out of 5 attempts.

The probability of making the three shots and missing the other two is:

$\frac{5!}{3!2!}0.8^3\times 0.2^2=\frac{5.4.3.2.1}{3.2.1\times2.1 }0.8^3\times 0.2^2\approx 0.205$

This is the probability of three successes in 5 attempts for a binomially
distributed random variable with probability of success on a single attempt of
$0.8$ .

Your notes/text book should provide a detailed explanation of why this is the
case.

RonL
April 21st 2006, 04:09 AM
CaptainBlack

Quote:

Originally Posted by munkeyb0i

2. A person is chosen at random from shoppers at a store. If the person's probability of having blonde hair and glasses is 2/25 and the probability of wearing glasses is 9/25, determine P(blonde hair|wears glasses).
The only thing I could do is do a venn diagram for this question and I'm not too sure if it's even right.

P(blond and glassess)=P(blong|glasses)P(glasses)

so:

2/25=P(blond|glasses).9/25

hence:

P(blond|glasses)=2/25.25/9=2/9

RonL