Answer: ![P(B\mid A)=\frac{3}{10}](https://tex.z-dn.net/?f=P%28B%5Cmid%20A%29%3D%5Cfrac%7B3%7D%7B10%7D)
Step-by-step explanation:
Since we have given that
A: getting the sum of number on both cubes is less than 10
B: getting the sum of numbers on both cubes is a multiple of 3
Conditional probability for event B given that A occurs first :
![P(B\mid A)=\frac{P(A\cap B )}{P(A)}](https://tex.z-dn.net/?f=P%28B%5Cmid%20A%29%3D%5Cfrac%7BP%28A%5Ccap%20B%20%29%7D%7BP%28A%29%7D)
A ={(1,1)(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(5,1)(5,2),(5,3),(5,4),(6,1)(6,2)(6,3)}
B={(1,2),(2,1),(4,2)(2,4),(3,3),(5,4)(4,5),(3,6),(6,3)}
![P(A)=\frac{30}{36}\\\\=\frac{5}{6}](https://tex.z-dn.net/?f=P%28A%29%3D%5Cfrac%7B30%7D%7B36%7D%5C%5C%5C%5C%3D%5Cfrac%7B5%7D%7B6%7D)
and
![P(B)=\frac{9}{36}=\frac{1}{4}](https://tex.z-dn.net/?f=P%28B%29%3D%5Cfrac%7B9%7D%7B36%7D%3D%5Cfrac%7B1%7D%7B4%7D)
and
![P(A\cap B)=\frac{9}{36}\\\\=\frac{1}{4}](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3D%5Cfrac%7B9%7D%7B36%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B4%7D)
So using the formula,
![P(B\mid A)\\\\=\frac{\frac{1}{4}}{\frac{5}{6}}\\\\=\frac{1\times 6}{5\times 4}\\\\=\frac{3}{10}](https://tex.z-dn.net/?f=P%28B%5Cmid%20A%29%5C%5C%5C%5C%3D%5Cfrac%7B%5Cfrac%7B1%7D%7B4%7D%7D%7B%5Cfrac%7B5%7D%7B6%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%5Ctimes%206%7D%7B5%5Ctimes%204%7D%5C%5C%5C%5C%3D%5Cfrac%7B3%7D%7B10%7D)