An urn contains 90 balls. It is known that 30 arc red and that each of the other 60 is either yellow or black. One ball will be drawn at random from the urn. Consider the following four options:

Option 1 We receive $1,000 if a red ball is drawn.

Option 2 We receive $1,000 if a yellow ball is drawn.

Option 3 We receive $ 1,000 if a yellow or black ball is drawn.

Option 4 We receive $1,000 if a red or black ball is drawn.

a. Explain why most people prefer option 1 over option 2 and also prefer option 3 over option 4.

b. If we prefer option 1 to option 2, explain why we should also prefer option 4 over option 3.