In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.
I tried to get the answer, but could not get as I considered the case mentioned above. I tried in this way :
- First case : 6 in first toss
- Second case : Any other no. in first toss, 6 in second toss
- Third case : Any other no. in first two tosses, 6 in third toss.
- Fourth case : 6 does not appear (he can't toss again as mentioned he can toss thrice only)
Do we need to consider this 4th case? Why or why not? I mean to ask is questions somehow denying to consider this 4th case or not?