In a game, a man wins Rs. 1000 if he gets an even number ≥4 on a fair die and loses Rs. 200 for getting any other number on the die. If he decides to throw the die until he wins or maximum of three times, then his expected gain/loss (in Rupees) is
A
38009loss
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B
38009gain
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C
0
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D
400gain
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Solution
The correct option is B38009gain Even number on a die ≥4 is 4,6 Let A be the event that either 4 or 6 appears on the die and B be the event that a number other than 4,6 appears on the die. Then P(A)=13 and P(B)=23
Possible sequence of events are A,BA,BBA,BBB
Let X be a random variable denoting the winning amount. X+1000+800+600−600P(X)1329427827