A single letter is selected at random from the word “$PROBABILITY$”. The probability that the selected letter is a vowel is

‘$A$’ draws two cards with replacement from a pack of $52$ cards and ‘$B$' throws a pair of dice what is the chance that ‘$A$’ gets both cards of same suit and ‘$B$’ gets total of $6$

The probability of $A, B, C$ solving a problem are $\frac{1}{3},\,\frac{2}{7},\,\frac{3}{8}$ respectively. If all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is

A fair coin is tossed repeatedly. If tail appears on first four tosses then the probability of head appearing on fifth toss equals

The probability that in a year of the $22^{nd}$ century chosen at random there will be $53$ Sundays is

A bag contains $3$ red and $7$ black balls, two balls are taken out at random, without replacement. If the first ball taken out is red, then what is the probability that the second taken out ball is also red