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Joint Entrance Examination
Mathematics
Probability
Question 201
Question 201 of 417
Medium
MCQ
Players A, B alternately throw a pair of dice, starting with A. A wins if he throws a total of 6 before B throws a total of 7. Find the probability A wins.
A
5
/
31
5/31
5/31
B
31
/
61
31/61
31/61
C
5
/
6
5/6
5/6
D
30
/
61
30/61
30/61
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Official solution
P
(
sum
=
6
)
=
5
36
P(\text{sum}=6)=\dfrac{5}{36}
P
(
sum
=
6
)
=
36
5
,
P
(
sum
=
7
)
=
1
6
P(\text{sum}=7)=\dfrac16
P
(
sum
=
7
)
=
6
1
. \[P(A\text{ wins}) = \frac{5/36}{1-\left(\frac{31}{36}\right)\left(\frac{30}{36}\right)} = \frac{5/36}{61/216} = \frac{30}{61}\]
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