Conditional Probability and Multiplication Theorem

Four persons draw $4$ cards from an ordinary pack. If the chance that a card is of each suit is $p_1$ and the chance that no two cards are of equal value is $p_2$ then the value of $\frac{p_1}{p_2}=$

$P\left(A\right)=\frac{2}{5},P\left(B\right)=\frac{3}{10},P\left(A\cap B\right)=\frac{1}{5}$ then $P\left(\frac{A^{\text{'}}}{B^{\text{'}}}\right) P\left(\frac{B^{\text{'}}}{A^{\text{'}}}\right)=\_\_\_\_$

$A$ and $B$ try to hit a target. The probability that $A$ hits the target is $\frac{7}{10}$ and the probability that $B$ hits the target is $\frac{4}{10}.$ If these two events are independent, the probability that $B$ hits the target, given that the target is hit, is

If two events $A$ and $B$ are such that $P\left(A^c\right)=0.3$, $P\left(B\right)=0.4$ and $P(A\cap B^c)=0.5$, then $P\left[\frac{B}{\left(A\cup B^c\right)}\right]$ is

A bag contains 5 white and 3 black balls. Two balls are drawn at random without replacement. Determine the probability of getting both the balls black.

Three faces of a fair die are yellow, two faces red and one blue. The die is thrown twice. The probability that $1^{st}$ throw will give an yellow face and the second a blue face is

There are 6 red and 5 black balls in a bag. Two balls are drawn at random one after another with replacement. The probability that both the balls drawn may be red is

If $6P\left(A\right)=8P\left(B\right)=14P\left(A\cap B\right)=1$, then the $\mathrm{P}\left(\frac{\overline{A}}{B}\right)=\dots \dots \dots .$

A bag contains $3$ Red balls and $3$ Blue balls. A ball is drawn from the bag and if it is of red colour, it is placed back in the bag and if it is of blue colour, it is placed back in the bag with an additional blue colour ball. Choose the correct statement.

If $P\left(A\right)=\frac{1}{2}, P\left(B\right)=\frac{1}{4} \text{and} P(A\cup B)=\frac{5}{8},$ then $P\left(\frac{B}{A}\right)=$

If two events $A$ and $B$ are such that $P\left(A\right)=0.3,P\left(B\right)=0.4, P\left(\overline{A}\cap \overline{B}\right)=0.5$, then the value of $P\left(\frac{B}{A\cup \overline{B}}\right)$ is equal to

Let $A$ and $B$ be two events such that $P\left(A\cap B\right)=\frac{1}{6}, P\left(\frac{A}{B}\right)=\frac{1}{2}$ and $P\left(\frac{B}{A}\right)=\frac{1}{3}$, then $P\left(\overline{A}\cap B\right)$ is equal to

If $P\left(E\right)=0.6, P\left(F\right)=0.3$ and $P(E\cap F)=0.2$, then find $P\left(F|E\right)$.

If $P\left(A\right)=0.6, P\left(B\right)=0.3$ and $P(A\cap B)=0.2$ then find $P\left(\frac{A}{B}\right)$

The letters of the word "$\mathrm{LOGARITHM}$" are arranged at random. The probability that arrangements starts with vowel and end with consonant is

A man is known to speak the truth $2$ out of $3$ times. If he throws a die and reports that it is six, then the probability that it is actually five is

When two dice are rolled, let $x$ be the probability of getting a sum of the numbers appear on the dice is at most $7$. Let $y$ be the probability of getting a sum $7$ at least once when a pair of dice are rolled $n$ times. In order to have $y>x,$ the minimum $n$ is

There are two bags, bag $1$ contains $3$ white and $2$ red balls and bag $2$ contains $4$ white and $5$ red balls. A ball is drawn randomly from bag $1$ and put in bag $2.$ Now $2$ balls are drawn from bag $2$ and found to be red. Then the probability that white ball was drawn from bag $1$ to bag $2$ is
 

A bag contains $6$ red balls and $10$ green balls. $3$ balls are drawn from it one by one randomly without replacement. If the $3^{\mathrm{rd}}$ drawn ball is red, then the probability that the first two drawn balls are green is