Multiplication Theorem ( Problems on conditional Probability)

Q. A box contains 5 black balls and 3 red balls. A total of three balls are picked from the box one after another, without replacing them back. The probability of getting two black balls and one red ball is

1. $\frac{3}{8}$
2. $\frac{2}{15}$
3. $\frac{15}{28}$
4. $\frac{1}{2}$

Q. Two dice are thrown simultaneously. The probability that the sum of numbers on both exceeds 8 is

1. $\frac{4}{36}$
2. $\frac{7}{36}$
3. $\frac{9}{36}$
4. $\frac{10}{36}$

Q. Two dice are thrown. What is the probability that the sum of the numbers on the two dice is eight?

1. $\frac{5}{36}$
2. $\frac{5}{18}$
3. $\frac{1}{4}$
4. $\frac{1}{3}$

Q. If $P\left(X\right)=\frac{1}{2};P\left(Y\right)=\frac{1}{3}andP\left(X/Y\right)=\frac{1}{3}thenP(X\cap Y)$ is

1. $\frac{1}{6}$
2. $\frac{1}{9}$
3. $\frac{1}{12}$
4. $\frac{1}{18}$