4 A fair six-sided dice is rolled repeatedly. Find the probability of the following events.
- A five occurs for the first time on the fourth roll.
- A five occurs at least once in the first four rolls.
- A five occurs for the second time on the third roll.
- At least two fives occur in the first three rolls.
The dice is rolled repeatedly until a five occurs for the second time.
- Find the expected number of rolls required for two fives to occur. Justify your answer.