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Question

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
38009 loss
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B
38009 gain
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C
0
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D
400 gain
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Solution

The correct option is B 38009 gain
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+600600P(X)1329427827

E(X)=1000×13+800×29+600×427600×827 =38009

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