Let a computer program generate only the digits $0$ and $1$ to form a string of binary numbers with probability of occurrence of $0$ at even places be $\frac{1}{2}$ and probability of occurrence of $0$ at the odd place be $\frac{1}{3}$. Then the probability that $'10'$ is followed by $'01'$ is equal to :

A box contains $10$ mangoes out of which $4$ are rotten. $2$ mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is

In a lottery there were $90$ tickets numbered $1$ to $90$. Five tickets were drawn at random. The probability that two of the tickets drawn numbers $15$ and $89$ is

Dialing a telephone number an old man forgets the last two digits remembering only that these are different dialled at random. The probability that the number is dialled correctly, is

If a leap year is selected at random, what is the change that it will contain $53$ Tuesdays ?

In four schools ${B_1},{B_2},{B_3},{B_4}$ the percentage of girls students is $12, 20, 13, 17$ respectively. From a school selected at random, one student is picked up at random and it is found that the student is a girl. The probability that the school selected is ${B_2},$ is