Question

Chapter 05, Section 5.4, Problem 029 Select each of the following experiments that are binomial experiments Drawing 3 balls without replacement from a box Selecting a few households from New York City and observing whether or not they own stocks when it is known that 4 % of all households in New York City own stocks. Drawing 3 balls with replacement from a box that contains 13 balls, 4 of which are red and 9 are blue, and observing the colors of the drawn balls that contains 13 balls, 4 of which are red and 9 are blue, and observing the colors of the drawn balls Click if you would like to Show Work for this question:

Answer 1

first is the only choice of binomial experiment.

As we know that the binomial distribution has the following formula

P(X=x) = nCx * p^x * q^(n-x)

here we have n=13 total balls , x=3 drawing balls without replacement

4 are of red color and 9 are of blue color

Now we may want to observe the event of blue

then the probability of success is p=9/13 and prob of failure is q=4/13 and we can put all the events in the above equation and solve

while for second option we don't have any of these values available as it's a test of Poission distribution

and in the case of last one where we have replacements allowed it's a Hyper Geometric distribution and hence we can't apply binomial theorm.

So.,

first is the only choice of binomial experiment.

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