A and B throw one dice for a stake of ` 11, which is to be won by the player who first throws a
six. The game ends when the stake is won by A or B. If A has the first throw, what are their
respective expectations?
(a) 5 and 6 (b) 6 and 5
(c) 11 and 0 (d) 9 and 2
Answers
Answer:
Step-by-step explanation:ANSWER
In his first throw A
′
s chance is
6
1
, in his second its is
6
5
×
6
5
×
6
1
,
because each players must have failed once before.
A can have a second throw, in his third throw his chance is (
6
5
)
4
×
6
1
because each players must have failed twice, and so on.
Thus A
′
s chance is the sum of the infinite series
6
1
(1+(
6
5
)
2
+(
6
5
)
4
+...)
Similarly B
′
s chance is the sum of the infinite series
6
5
.
6
1
(1+(
6
5
)
2
+(
6
5
)
4
)
Therefore A
′
s chance is to B
′
s as 6 is to 5;
their respective chance are therefore
11
6
and
11
5
and their expectation are rs6 and rs5 respectively.
I HOPE IT HELPS YOU
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MATHS
A and B throw with one die for a stake of Rs.11 which is to be won by the player who first throw 6. If A has the first throw, what are their respective expectations?
December 20, 2019
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Jayeeta Gulati
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ANSWER
In his first throw A
′
s chance is
6
1
, in his second its is
6
5
×
6
5
×
6
1
,
because each players must have failed once before.
A can have a second throw, in his third throw his chance is (
6
5
)
4
×
6
1
because each players must have failed twice, and so on.
Thus A
′
s chance is the sum of the infinite series
6
1
(1+(
6
5
)
2
+(
6
5
)
4
+...)
Similarly B
′
s chance is the sum of the infinite series
6
5
.
6
1
(1+(
6
5
)
2
+(
6
5
)
4
)
Therefore A
′
s chance is to B
′
s as 6 is to 5;
their respective chance are therefore
11
6
and
11
5
and their expectation are rs6 and rs5 respectively
Step-by-step explanation:
.
.
Its helps you