Please Explain! An urn contain
Please Explain!
An urn contains seven chips labeled 1,2,…,7. Three of thechips are black, two are red, and two are green. The chips aredrawn randomly one at a time without replacement until the urn isempty. Answer both questions for i = 1,…,7.
a. What is the probability that ith draw is chip 5?
b. What is the probability that ith draw is black?
Answer:
a. There are 7 numbers which have equal probability of beingdrawn.
Thus the probability that the first chip is chip 5 is 1/7.
If the first chip is not chip 5 (whose probability is 6/7), theprobability that the second chip is chip 5 is 1/6. Thus theprobability that the second chip is chip 5 is again 1/7 and soon.
The probability that the ith draw is chip 5 is therefore1/7.
b. There are three black and four non black chips.
The probability that the first draw is black is 3/7.
If the first draw is black, the probability that the second isalso black is 2/6 while if the first draw is not black, theprobability that the second is black is 3/6. Thus the probabilitythat the second draw is black = 3/7 * 2/6 + 4/7 * 3/6 = 18/42 =3/7.
Similarly the probability that the third draw is black is 3/7 *2/6 * 1/5 + 3/7 * 4/6 * 2/5 + 4/7 * 3/6 * 2/5 + 4/7 * 3/6 * 3/5 =90/210 = 3/7 and so on.
Therefore, the probability that the ith draw is black is3/7.
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