$A$ person goes to office by car, scooter, bus, and train, the probabilities of which are $1/7, 3/7, 2/7,$ and $1/7$ respectively. The probability that he reaches office late if he takes a car, scooter, bus, or train is $2/9, 1/9, 4/9,$ and $1/9$ respectively. Given that he reached the office in time, the probability that he travelled by car is: (in $/7$)

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:

An instructor has a question bank consisting of $300$ easy True / False questions,$200$ difficult True / False questions,$500$ easy multiple choice questions,and $400$ difficult multiple choice questions. If a question is selected at random from the question bank,what is the probability that it will be an easy question given that it is a multiple choice question?

In a test,a student either guesses,copies,or knows the answer to a multiple-choice question with four choices. The probability that he guesses is $1/3$ and the probability that he copies the answer is $1/6$. The probability that his answer is correct,given that he copied it,is $1/8$. The probability that he knew the answer to the question,given that he answered it correctly,is

$A, B_1, B_2, B_3$ are the events in a random experiment. If $P(B_1)=0.25, P(B_2)=0.30, P(B_3)=0.45, P(A|B_1)=0.05, P(A|B_2)=0.04, P(A|B_3)=0.03$, then $P(B_2|A) = $

Two groups are competing for the position on the board of directors of a corporation. The probabilities that the first and the second groups will win are $0.6$ and $0.4$ respectively. Further,if the first group wins,the probability of introducing a new product is $0.7$ and the corresponding probability is $0.3$ if the second group wins. Find the probability that the new product was introduced by the second group. (in $/9$)