Two dice are thrown. What is the probability that difference of numbers on them is 2 or 3 ?

What is the mean of the numbers 1, 2, 3, ... 10 with frequencies ⁹C₀, ⁹C₁, ⁹C₂ ..., ⁹C₉, respectively?

The probability that a person recovers from a disease is 0.8. What is the probability that exactly 2 persons out of 5 will recover from the disease?

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?