<h2>
Answer:</h2>
<em>(a).
</em>
<em>(b).
</em>
<h2>
Step-by-step explanation:</h2>
(a).
The number of Black marbles in the bag = 8
Number of White marbles in the bag = 5
Number of Yellow marbles in the bag = 3
Total marbles in the bag = 16
The probability is given by,
![Probability=\frac{Favourable\ outcomes}{Total\ Possibilities}](https://tex.z-dn.net/?f=Probability%3D%5Cfrac%7BFavourable%5C%20outcomes%7D%7BTotal%5C%20Possibilities%7D)
So,
Probability of drawing a<u> Black Marble first</u> is,
![Probability=\frac{8}{16}=\frac{1}{2}](https://tex.z-dn.net/?f=Probability%3D%5Cfrac%7B8%7D%7B16%7D%3D%5Cfrac%7B1%7D%7B2%7D)
Now replacement is done.
So,
Probability of drawing <u>Yellow Marble second</u> is,
![Probability=\frac{3}{16}](https://tex.z-dn.net/?f=Probability%3D%5Cfrac%7B3%7D%7B16%7D)
So,
<u>Probability is given by,</u>
![Probability=\frac{1}{2}\times \frac{3}{16}\\Probability=\frac{3}{32}](https://tex.z-dn.net/?f=Probability%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%5Cfrac%7B3%7D%7B16%7D%5C%5CProbability%3D%5Cfrac%7B3%7D%7B32%7D)
<em><u>Therefore, the probability is,</u></em>
![Probability=\frac{3}{32}](https://tex.z-dn.net/?f=Probability%3D%5Cfrac%7B3%7D%7B32%7D)
(b).
Number of Red marbles = 5
Number of Yellow marbles = 3
Number of White marbles = 8
Total marbles = 46
Probability of drawing a <u>Red marble first</u> is given by,
![Probability=\frac{5}{16}](https://tex.z-dn.net/?f=Probability%3D%5Cfrac%7B5%7D%7B16%7D)
And,
Probability of drawing a <u>White marble second</u> is given by,
![Probability=\frac{8}{15}](https://tex.z-dn.net/?f=Probability%3D%5Cfrac%7B8%7D%7B15%7D)
As, there is no replacement.
So,
Probability is given by,
![Probability=\frac{5}{16}\times \frac{8}{15}\\Probability=\frac{1}{6}](https://tex.z-dn.net/?f=Probability%3D%5Cfrac%7B5%7D%7B16%7D%5Ctimes%20%5Cfrac%7B8%7D%7B15%7D%5C%5CProbability%3D%5Cfrac%7B1%7D%7B6%7D)
<em><u>Therefore, the Probability is given by,</u></em>
![Probability=\frac{1}{6}](https://tex.z-dn.net/?f=Probability%3D%5Cfrac%7B1%7D%7B6%7D)