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JEE Advanced 2020 Full Test 6 Paper 2
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© examsnet.com
Question : 50
Total: 54
Die A has 4 red and 2 white faces whereas die B has 2 red and 4 white faces. A coin is flipped once. If it shows a head, the game continues by throwing die
A
,
if it shows tail, then die
B
is to be used. If the probability that die
A
is used is
32
∕
33
.
When it is given that red throws up every time in first
n
throws, then find the value of
n
?
4
5
6
7
Validate
Solution:
Let
R
be the event that a red face appears in each of the first
n
throws,
E
1
:
Die
A
is used when head has already fallen
E
2
:
Die
B
is used when tail has already fallen
∴
P
(
R
E
s
)
=
(
2
3
)
n
&
P
(
R
E
2
)
=
(
1
3
)
n
As per the given condition,
p
(
E
1
)
⋅
p
(
R
E
1
)
P
(
E
2
)
⋅
(
P
R
∕
E
4
)
+
P
(
E
2
)
,
P
(
R
E
2
)
=
32
33
1
2
⋅
(
2
9
)
n
1
2
(
2
3
)
n
+
1
2
⋅
(
1
3
)
n
=
32
33
n
=
5
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