**Solution:**

The given no. of outcomes when die is thrown

(i) If 2 appears on the roll of the die.

Therefore, the first roll have 5 outcomes each and roll results 2

No. of outcomes

(ii) If it is considered that 2 appears not later than roll of the die, then 2 comes before roll.

If 2 appears in first roll, no. of ways

If 2 appears in second roll, no. of ways

(as first roll doesn’t result in 2

If 2 appears in third roll, no. of ways

(as first two rolls doesn’t result in 2 )

In the similar way if 2 appears in roll, no. of ways times

The possible outcomes if 2 appears before roll are

(i) How many elements of the sample space correspond to the event that the 2 appears on the roll of the die?

(ii) How many elements of the sample space correspond to the event that the 2 appears not later than the roll of the die?

(i) How many elements of the sample space correspond to the event that the 2 appears on the roll of the die?

(ii) How many elements of the sample space correspond to the event that the 2 appears not later than the roll of the die?