<p>I’m having some difficulties with probability Q’s.
Can someone please explain these two problems to me?</p>
<li><pre><code>A jar contains two black marbles and one white marble. If a marble is selected from the jar and removed and then a second marble is selected from the jar, what is the probability that the second marble selected is white?
</code></pre></li>
<li><p>If a fair coin is flipped three times, what is the probability that the result will be tails exactly twice? <—This one calls for drawing it out, but what’s the method to solve it mathematically?</p></li>
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<p>For 17, there is a 2/3 chance that it is not white for the first draw and then a 1/2 chance that it is white so multiply then and its 1/3 chance.</p>
<ol>
<li>You kind of have to draw this one but you know that any outcome is 1/8 chance and for 2 of the same occur 6 out of those 8 times, but half those are two heads and half are tails. So that is 3 times it can be 2 tails so 3/8 chance.</li>
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<p>17:
Case I: (P=1/3) => White Marble is drawn. Thus, probability of white marble on second draw=0
Case II (P=2/3) => Black marble is drawn. Thus, probability of white marble on second draw=1/2</p>
<p>0 * 1/3 + 1/2 * 2/3 = 1/3</p>
<p>23:</p>
<p>3 choose 2 * (1/2)^3 = 3/8</p>
<p>(this is just binomial theorem....read up on it! It's important and easy!)</p>
<p>For example. If you were rolling a die and seeing the probability of rolling a 5 exactly nine times after twenty-two rolls:
(22 choose 9) * (1/6)^9 * (5/6)^(22-9)
or....
(number of combos) * (probablility)^n * (1-probability)^(k-n)
google it!</p>
<p>to degeneration:</p>
<p>it's binompdf(n,p,k) i think ... so binompdf(3,.5,2) unless I am mistaken. (For those who are confused binompdf uses the binomial theoren for an exact problem, whereas binomcdf uses it for a non-exact problem. For example, a binomcdf would find the chances of getting two or less heads, not just the probability of an event but a bunch of events.)</p>
<p>Thanks for the quick responses. I feel like a moron for not understanding problem 17 :(.
The binomial theorem looks complex, will definitely try to ingrain that into my mind.</p>
<p>3 choose 2 is simply the counter for the number of possibilites .. you have 3 picks and need to choose 2 that are tails:
3 choose 2 finds....
TTH
THT
HTT
so 3 choose 2 = 3 .. the count of how many ways the event can be arranged.</p>
<p>refer to my above post and see (number of combos)<em>(p)^(n)</em>(1-p)^(k-n) = total probability</p>