Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The chance that the design is faulty is 10%. The chance that the building collapses is 95% if the design is faulty, otherwise it is 45%. If it is seen that the building has collapsed, then what is the probability that it is due to faulty design?

A fair coin is tossed 6 times. What is the probability of getting a result in the 6^th toss which is different from those obtained in the first five tosses ?

In a class, there are n students including the students P and Q. What is the probability that P and Q sit together if seats are assigned randomly?

Consider the following for the next items that follow:

Three boys P, Q, R and three girls S, T, U are to be arranged in a row for a group photograph.

What is the probability that all three boys sit together?