Answer:
Following are the answer to this question:
Step-by-step explanation:
In the question first calls the W if the transmitted chip was white so, the W' transmitted the chip is red or R if the red chip is picked by the urn II.
whenever a red chip is chosen from urn II, then the probability to transmitters the chip in white is:
![P(\frac{w}{R}) = \frac{P(W\cap R)}{P(R)} \ \ \ \ \ _{Where}\\\\P(R) = P(W\cap R) + P(W'\cap R) \\](https://tex.z-dn.net/?f=P%28%5Cfrac%7Bw%7D%7BR%7D%29%20%3D%20%5Cfrac%7BP%28W%5Ccap%20R%29%7D%7BP%28R%29%7D%20%20%5C%20%5C%20%5C%20%5C%20%5C%20_%7BWhere%7D%5C%5C%5C%5CP%28R%29%20%3D%20P%28W%5Ccap%20R%29%20%2B%20P%28W%27%5Ccap%20R%29%20%5C%5C)
The probability that only the transmitted chip is white is therefore
, since urn, I comprise 3 chips and 2 chips are white.
But if the chip is white so, it is possible that urn II has 4 chips and 2 of them will be red since urn II and 2 are now visible, and it is possible to be:
![P(W\cap R) = P(W) \times P(\frac{R}{W}) \\](https://tex.z-dn.net/?f=P%28W%5Ccap%20R%29%20%3D%20P%28W%29%20%5Ctimes%20P%28%5Cfrac%7BR%7D%7BW%7D%29%20%5C%5C)
![= \frac{2}{3}\times \frac{2}{4} \\\\= \frac{2}{3}\times \frac{1}{2} \\\\= \frac{2}{3}\times \frac{1}{1} \\\\=\frac{1}{3}\\\\= 0.333](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B2%7D%7B3%7D%5Ctimes%20%5Cfrac%7B2%7D%7B4%7D%20%5C%5C%5C%5C%3D%20%5Cfrac%7B2%7D%7B3%7D%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%5C%5C%3D%20%5Cfrac%7B2%7D%7B3%7D%5Ctimes%20%5Cfrac%7B1%7D%7B1%7D%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B3%7D%5C%5C%5C%5C%3D%200.333)
Likewise, the chip transmitted is presumably red
and the chip transferred is a red chip of urn II
, and a red chip is likely to be red
.
Finally, ![P(W'\cap R) = P(W') \times P(\frac{R}{W'})\\](https://tex.z-dn.net/?f=P%28W%27%5Ccap%20R%29%20%3D%20P%28W%27%29%20%5Ctimes%20P%28%5Cfrac%7BR%7D%7BW%27%7D%29%5C%5C)
![= \frac{1}{3} \times \frac{3}{4} \\\\ = \frac{1}{1} \times \frac{1}{4} \\\\=\frac{1}{4}\\\\= 0.25](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20%5Cfrac%7B3%7D%7B4%7D%20%5C%5C%5C%5C%20%3D%20%5Cfrac%7B1%7D%7B1%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7B4%7D%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5C%3D%200.25)
The estimation of
and
as:
![P(R) = 0.3333 + 0.25\\\\ \ \ \ \ \ \ \ \ \ = 0.5833 \\\\ P(\frac{W}{R}) = \frac{0.3333}{0.5833} \\\\\ \ \ \ \ \ \ = 0.5714](https://tex.z-dn.net/?f=P%28R%29%20%3D%200.3333%20%2B%200.25%5C%5C%5C%5C%20%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%3D%200.5833%20%5C%5C%5C%5C%20P%28%5Cfrac%7BW%7D%7BR%7D%29%20%3D%20%5Cfrac%7B0.3333%7D%7B0.5833%7D%20%5C%5C%5C%5C%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%3D%200.5714)