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JEE Main Math Class 12 Probability Part 2 Questions
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© examsnet.com
Question : 2
Total: 95
In a tournament, a team plays 10 matches with probabilities of winning and losing each match as
1
3
and
2
3
respectively. Let
x
be the number of matches that the team wins, and
y
be the number of matches that team loses. If the probability
P
(
|
x
−
y
|
≤
2
)
is
p
, then
3
9
p
equals........
[4 Apr 2024 Shift 2]
Your Answer:
Validate
Solution:
👈: Video Solution
P
(
W
)
=
1
3
P
(
L
)
=
2
3
x
=
number of matches that team wins
y
=
number of matches that team loses
|
x
−
y
|
≤
2
and
x
+
y
=
10
|
x
−
y
|
=
0
,
1
,
2
x
,
y
∈
N
Case-I
:
|
x
−
y
|
=
0
⇒
x
=
y
∵
x
+
y
=
10
⇒
x
=
5
=
y
P
(
|
x
−
y
|
=
0
)
=
10
C
5
(
1
3
)
5
(
2
3
)
5
Case-II
:
|
x
−
y
|
=
1
⇒
x
−
y
=
±
1
Case-III :
|
x
−
y
|
=
2
⇒
x
−
y
=
±
2
x
−
y
=
2
OR
x
−
y
=
−
2
∵
x
+
y
=
10
∵
x
+
y
=
10
x
=
6
,
y
=
4
x
=
4
,
y
=
6
P
(
|
x
−
y
|
=
2
)
=
10
C
6
(
1
3
)
6
(
2
3
)
4
+
10
C
4
(
1
3
)
4
(
2
3
)
6
p
=
10
C
5
2
5
3
10
+
10
C
6
2
4
3
10
+
10
C
4
2
6
3
10
3
9
p
=
1
3
(
10
C
5
2
5
+
10
C
6
2
4
+
10
C
4
2
6
)
=
8288
© examsnet.com
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