Q99 / 200 · Manipal (MET) 2010 · Mathematics

The least number of times a fair coin must be tossed so that the probability of getting atleast one head is atleast 0.8 is

  • A
    7
  • B
    6
  • C
    5
  • Correct answer
    D
    3

Solution

Suppose the coin is tossed $n$ times. Let $X$ be the number of the heads obtained. Then, $X$ follows a binomial distribution with parameters $n$ and $p=\frac{1}{2}$ Now, $P(X \geq 1) \geq 0.8 \Rightarrow 1-P(X=0) \geq 0.8$ $\Rightarrow \quad 1-{ }^n C_0 p^0(1-p)^n \geq 0.8$ $\Rightarrow \quad\left(\frac{1}{2}\right)^n \leq 0.2$ or $\left(\frac{1}{2}\right)^n \leq \frac{1}{5}$ $\Rightarrow \quad 2^n \geq 5$ $\Rightarrow \quad n \geq 3$ Hence, the least value of $n$ is 3 .

Hence, the correct answer is option: 'D'.

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