The probability that a person goes to college by car is $\frac{1}{5}$,by bus is $\frac{2}{5}$,and by train is $\frac{3}{5}$. The probabilities that he reaches the college late if he takes a car,bus,or train are $\frac{2}{7}$,$\frac{4}{7}$,and $\frac{1}{7}$ respectively. If he reaches the college in time,the probability that he traveled by car is:

Box $I$ contains $30$ cards numbered $1$ to $30$ and Box $II$ contains $20$ cards numbered $31$ to $50$. $A$ box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box $I$ is

$A$ letter is known to have come either from $LONDON$ or $CLIFTON$; on the postmark only the two consecutive letters $ON$ are legible. The probability that it came from $LONDON$ is

Two bags $A$ and $B$ contain $2$ white,$3$ black,$4$ red balls and $3$ white,$4$ black,$5$ red balls respectively. $A$ ball is drawn from bag $A$ and transferred to bag $B$. If a ball is then drawn from bag $B$,what is the probability that the ball drawn from bag $B$ is white?

Recent studies suggest that $12\%$ of the world population is left-handed. Depending on parents' hand usage, the chances of having left-handed children are as follows: $A$. Both parents are left-handed, chances of having left-handed children = $24\%$. $B$. Both parents are right-handed, chance of having left-handed children = $9\%$. $C$. Father left-handed and mother right-handed, chances of having left-handed children = $17\%$. $D$. Father right-handed and mother left-handed, chances of having left-handed children = $22\%$. Given $P(A) = P(B) = P(C) = P(D) = 1/4$ and $L$ denotes the event that the child is left-handed. What is the probability $P(A|L)$?

Of the students in a college,it is known that $60 \%$ reside in a hostel and $40 \%$ are day scholars (not residing in a hostel). Previous year results report that $30 \%$ of all students who reside in a hostel attain $A$ grade and $20 \%$ of day scholars attain $A$ grade in their annual examination. At the end of the year,one student is chosen at random from the college and they have an $A$ grade. What is the probability that the student is a hostler?