$A$ bag $P$ contains $5$ white marbles and $3$ black marbles. Four marbles are drawn at random from $P$ and are put in an empty bag $Q$. If a marble drawn at random from $Q$ is found to be black,then the probability that all the three black marbles in $P$ were transferred to the bag $Q$ is:

$A$ boy speaks the truth in $3$ out of $5$ times. If he throws a die and reports that the number appeared on it is $5$, then the probability that it is actually $5$ is:

Assume that the probability of a patient having a heart attack is $40 \%$. It is also assumed that a meditation and yoga course reduces the risk of a heart attack by $30 \%$ and the prescription of a certain drug reduces its risk by $25 \%$. $A$ patient can choose any one of the two options with equal probability. Given that a patient selected at random suffers a heart attack after choosing one of the two options,find the probability that the patient followed the course of meditation and yoga.

Bag $A$ contains $6$ Green and $8$ Red balls and bag $B$ contains $9$ Green and $5$ Red balls. $A$ card is drawn at random from a well-shuffled pack of $52$ playing cards. If it is a spade,two balls are drawn at random from bag $A$,otherwise two balls are drawn at random from bag $B$. If the two balls drawn are found to be of the same colour,then the probability that they are drawn from bag $A$ is

$A$ pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade is:

$A$ doctor is to visit a patient. From past experience,it is known that the probabilities that he will come by train,bus,scooter,or by other means of transport are respectively $\frac{3}{10}, \frac{1}{5}, \frac{1}{10},$ and $\frac{2}{5}$. The probabilities that he will be late are $\frac{1}{4}, \frac{1}{3},$ and $\frac{1}{12}$ if he comes by train,bus,and scooter respectively,but if he comes by other means of transport,then he will not be late. When he arrives,he is late. What is the probability that he comes by train?