Statistics And Probability Question 365
Question: A fair coin is tossed n times. If the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then n is equal to
[Kurukshetra CEE 1998; AMU 2000]
Options:
A) 15
B) 14
C) 12
D) 7
Show Answer
Answer:
Correct Answer: B
Solution:
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Probability that head occurs 6 times $ ={}^{n}C_6{{( \frac{1}{2} )}^{6}}{{( \frac{1}{2} )}^{n-6}} $ and probability that head occurs 8 times $ ={}^{n}C_8{{( \frac{1}{2} )}^{8}}{{( \frac{1}{2} )}^{n-8}} $
$ \therefore ,{}^{n}C_6{{( \frac{1}{2} )}^{6}}{{( \frac{1}{2} )}^{n-6}}={}^{n}C_8{{( \frac{1}{2} )}^{8}}{{( \frac{1}{2} )}^{n-8}} $ $ {}^{n}C_6={}^{n}C_8 $
Þ $ (n-6)(n-7)=56\Rightarrow n=14 $ .
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