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Mathematics
OpenStudy (anonymous):

@jim_thompson5910 can U help me with a couple probability questions

OpenStudy (anonymous):

okay here is the first one

OpenStudy (anonymous):

okay here is the first one ????

OpenStudy (anonymous):

Approximately 3% of peanuts in a certain shipment are spoiled. If you randomly select 24 peanuts, what is the probability that exactly two are spoiled?

OpenStudy (anonymous):

okay how abt this question: If a 6-sided die is rolled 8 times, what is the probability of getting exactly one 6? Give your answer to the nearest thousandth.

OpenStudy (anonymous):

@Mertsj can u help me?

OpenStudy (mertsj):

Wouldn't it be 1- probability of getting a "non-6"?

OpenStudy (anonymous):

you can do it with binomial, have you done binomial?

OpenStudy (anonymous):

yes but i need help

OpenStudy (anonymous):

n=8, p= 1/6

OpenStudy (mertsj):

So I think it would be 1-(5/6)^8

OpenStudy (anonymous):

in this case you dont actually need it as its relatively simple to count the options the possible outcomes, with "6" being a 6 and "N" being not a 6 : NNNNNNN6 NNNNNN6N NNNNN6NN NNNN6NNN NNN6NNNN NN6NNNNN N6NNNNNN 6NNNNNNN so we have 8 possibilities each with (1/6)*((5/6)^7) probability so 8* (1/6)*((5/6)^7) alternatively using binomial p = 1/6 , n = 8 , x = 1 \[P(X=x) = C(p^x(1-p)^{n-x})\] where C is "n choose x" so we have P(X=1) = 8((1/6)((5/6)^7))

OpenStudy (anonymous):

@Mertsj i think that would be " probability that there is at least one 6"

OpenStudy (anonymous):

so 0.372

OpenStudy (anonymous):

yes :)

OpenStudy (mertsj):

Yes, you are correct, eigneschmeigen. I never was any good at probability.

OpenStudy (anonymous):

can u help em with one more: 1.Two coins are tossed 20 times and the number of times that both of the coins land tails is recorded. 2. In a light-bulb manufacturing plant, the probability of a bulb being defective is 0.2%. A sample of 100 bulbs is chosen at random and the number of defective bulbs recorded. 3. A card is drawn from a well-shuffled standard deck of cards and the suit is recorded. This is repeated 10 times and the cards are not replaced after each draw. 4. A 10-question multiple-choice test has 4 possible answers for each question. A student guesses the first 9 answers randomly but is certain of the answer to the tenth question. The number of correct answers is recorded. 5. A basketball player makes 85% of her free throws. In a particular game she has 10 free throws. The number of free throws that she makes is recorded.

OpenStudy (anonymous):

which is a binomial distribution

OpenStudy (anonymous):

probability is tricky, always used to catch me out, one of my exams include probability recently so i'm a bit warmed up on it

OpenStudy (anonymous):

@eigenschmeigen u live in canada.. if u dont mind me askin

OpenStudy (anonymous):

no, i like in england. i have a few canadian friends though conditions for X ~ B(n,p) 1: The number of observations n is fixed. 2: Each observation is independent. 3: Each observation represents one of two outcomes ("success" or "failure"). 4: The probability of "success" p is the same for each outcome.

OpenStudy (anonymous):

so 1,2,and 5

OpenStudy (anonymous):

yeah i think so

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