JEE MAIN - Mathematics (2021 - 25th July Evening Shift - No. 22)
A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is ______________.
Answer
4
Explanation
P(Head) = $${1 \over 2}$$
1 $$-$$ P(All tail) $$\ge$$ 0.9
$$1 - {\left( {{1 \over 2}} \right)^n}$$ $$\ge$$ 0.9
$$ \Rightarrow {\left( {{1 \over 2}} \right)^n} \le {1 \over {10}}$$
$$\Rightarrow$$ nmin = 4
1 $$-$$ P(All tail) $$\ge$$ 0.9
$$1 - {\left( {{1 \over 2}} \right)^n}$$ $$\ge$$ 0.9
$$ \Rightarrow {\left( {{1 \over 2}} \right)^n} \le {1 \over {10}}$$
$$\Rightarrow$$ nmin = 4
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