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?

If r is the coefficient of correlation between x and y, then what is the correlation coefficient between (3x + 4) and (-3y + 3)?

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 ?

If H is the Harmonic Mean of three numbers 10C4, 10C5, and 10C6, then what is the value of $\frac{270}{H}$ ?