Question 326205
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(a) There is a pool of 8 people to choose from, and 4 of them are not Republicans.  So the probability that the first person chosen will not be a Republican is *[tex \Large \frac{4}{8}].


Once the first person is chosen and it is, in fact, not a Republican, then you now have a pool of 7 people from which to choose, 3 of which are not Republicans.  So the probability that the second person chosen will not be a Republican given that the first was not a Republican is *[tex \Large \frac{3}{7}].


The total probability is the product: *[tex \Large \left(\frac{4}{8}\right)\left(\frac{3}{7}\right)\ =\ \frac{12}{56}\ =\ \frac{3}{14}]


(b) There is a pool of 8 people to choose from, and 4 of them are  Republicans.  So the probability that the first person chosen will be a Republican is *[tex \Large \frac{4}{8}].


Once the first person is chosen and it is, in fact, a Republican, then you now have a pool of 7 people from which to choose, 3 of which are Republicans.  So the probability that the second person chosen will be a Republican given that the first was a Republican is *[tex \Large \frac{3}{7}].


The total probability is the product: *[tex \Large \left(\frac{4}{8}\right)\left(\frac{3}{7}\right)\ =\ \frac{12}{56}\ =\ \frac{3}{14}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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