Two persons A and B are rolling two dice on
the condition that the person who gets 3 will
win the game. If A starts the game, then find
the probability of A and B respectively to win
the game.
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Answer ⤵️
Probability of win=
6
1
Probability of lose =
6
5
if A starts the game
Probability that A wins =
6
1
+
6
5
×
6
5
×
6
1
+
6
5
×
6
5
×
6
5
×
6
5
×
6
1
......... so on
=
6
1
[1+(
6
5
)
2
+(
6
5
)
4
......]
Using infinite GP, we get
Probability that A wins
6
1
×
1−(
6
5
)
2
1
=
11
6
Probability that B wins =1−
11
6
=
11
5
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