QJEEM19Ma1d55: JEE Main 2019 Mathematics - Class 12 JEEM19Ma1d55 Solution: The minimum number of times one has to toss a fair coin so that …

Probablity of getting head P(H) = $$\frac{1}{2}$$

Probablity of getting tail P(T) = 1 - $$\frac{1}{2}$$ = $$\frac{1}{2}$$

Probability of observing at least one head out of n tosses

= 1 - Probability of observing no head occurs out of n tosses

= 1 - $${\left(\frac{1}{2}\right)}^n$$

According to the question,

1 - $${\left(\frac{1}{2}\right)}^n$$ $$\ge$$ $$\frac{90}{100}$$

$$\Rightarrow$$ $${\left(\frac{1}{2}\right)}^n\le \frac{1}{10}$$

$$\Rightarrow$$ $$2^n\ge 10$$

As 2³ = 8

2⁴ = 16

$$\therefore$$ Minimum value of n = 4