Questions

Non collision can happen only when all the cars move in same direction.

That is either all cars moving in clockwise direction or all cars moving in anti clockwise direction.
P(all cars not colliding)

= P(all cars moving in the same direction)

= P(all cars moving in clockwise direction)  +  P(all cars moving in anticlockwise direction)

= [p(A --> C) x p(C --> B) x p(B --> A)]  +  [p(A --> B) x p(B --> C) x p(C --> A)]

= [1/2 x 1/2 x 1/2] + [1/2 x 1/2 x 1/2]

= 1/8 + 1/8

= 1/4

Since they can do 19 programs in 19 hours, Then 52 programs in 52 hours respectively.
And a 15 min interval
Total time they take to do 52 programs is 52 hours 15 minutes.

The required number 100.

It is not an odd number and is not higher than 100 and greater than 90.

When we subtract 100 from 100, we get nothing i.e, 0.

In message passing, it is the condition in which, both, the sender and receiver are blocked until the message is delivered.