An experiment consists of rolling a die until a 2 appears.
(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?
An experiment consists of rolling a die until a 2 appears.
(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?

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