two cubic dice are cast simultaneously. a person get 5 rupees if the number on the first dice is greater than that on the second dice .he get rupees 10 if both number are equal otherwise he loose rupees 7 the entry fee for the game is rupees 4 .find his expected gain and not expected amount
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Step-by-step explanation:
Correct option is A)
In a throw of a die, the probability of getting a six is
6
1
and the probability of not getting a 6 is
6
5
Three cases can be obtain.
i. If he gets a six in the first throw, then the required probability is
6
1
.
Amount he will receive =1 Rs
ii. If he does not get a six in the first throw and gets a six in the second throw, then probability =(
6
5
×
6
1
)=
36
5
Amount he will receive =−1+1=0 Rs.
iii. If he does not get a six in the first two throws and gets a six in the third throw, then probability =(
6
5
×
6
5
×
6
1
)=
216
25
Amount he will receive = -Re 1 - Re 1 + Re 1 = -1
Expected value he can win =
6
1
(1)+(
6
5
×
6
1
)(0)+[(
6
5
)
2
×
6
1
](−1)
=
216
36−25
=
216
11
=0.05
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