Statistics And Probability Question 464
Question: At least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8, is
Options:
A) 7
B) 6
C) 5
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
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Suppose the coin tossed $ n $ times. Let $ X $ be the number of heads obtained. Then $ X $ follows a binomial distribution with parameters $ n $ and $ p=\frac{1}{2}. $ We have, $ P(X\ge 1)\ge 0.8\Rightarrow 1-P(X=0)\ge 0.8 $
Þ $ 1{{-}^{n}}C_0P^{0}{{(1-P)}^{n}}\ge 0.8 $
$ \Rightarrow {{( \frac{1}{2} )}^{n}}\le 0.2\Rightarrow {{( \frac{1}{2} )}^{n}}=\frac{1}{5}\Rightarrow 2^{n}\ge 5 $ This shows that the least value of n is 3.
BETA
