Probability Question 141
Question: A coin is tossed n times. The probability of getting head at least once is greater than 0.8, then the least value of n is
[EAMCET 2003]
Options:
A) 2
B) 3
C) 4
D) 5
Show Answer
Answer:
Correct Answer: B
Solution:
Let X be the number of heads getting. X follows binomial distribution with parameters $ n,p=1/2 $
Given that $ P(X\ge 1)\ge 0.8 $
Therefore $ 1-P(X=0)\ge 0.8\Rightarrow P(X=0)\le 0.2 $
Therefore$ ^{n}C_0{{(1/2)}^{n}}\le 0.2 $
$ \Rightarrow $
$ \frac{1}{2^{n}}\le \frac{1}{5}\Rightarrow 2^{n}=5. $
$ \therefore $ The least value of $ n $ is 3.
BETA
