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Joint Entrance Examination
Mathematics
Probability
Question 271
Question 271 of 417
Medium
MCQ
In
B
(
n
,
1
4
)
B(n,\dfrac14)
B
(
n
,
4
1
)
, if
P
(
at least one success
)
≥
9
10
P(\text{at least one success})\ge\dfrac{9}{10}
P
(
at least one success
)
≥
10
9
, find
n
n
n
in terms of logs.
A
1
log
10
4
+
log
10
3
\dfrac{1}{\log_{10}4+\log_{10}3}
lo
g
10
4
+
lo
g
10
3
1
B
9
log
10
4
−
log
10
3
\dfrac{9}{\log_{10}4-\log_{10}3}
lo
g
10
4
−
lo
g
10
3
9
C
4
log
10
4
−
log
10
3
\dfrac{4}{\log_{10}4-\log_{10}3}
lo
g
10
4
−
lo
g
10
3
4
D
1
log
10
4
−
log
10
3
\dfrac{1}{\log_{10}4-\log_{10}3}
lo
g
10
4
−
lo
g
10
3
1
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Official solution
\[1-\left(\frac34\right)^n\ge\frac{9}{10} \implies \left(\frac34\right)^n\le\frac{1}{10} \implies n\ge\frac{1}{\log_{10}4-\log_{10}3}\]
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