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

Probability of getting at least one head = 1 - Probability of getting no heads = 1 - Probability of getting all tails.

Let the number of times the coin be tossed be n.

Probability of getting one tail =$$\dfrac{1}{2}$$

So, probability of getting all tails in n trials = $$\left(\dfrac{1}{2}\right)^n$$

So, probability of getting at least one head = $$1-\left(\dfrac{1}{2}\right)^n$$

According to question,

$$1-\left(\dfrac{1}{2}\right)^n>0.8$$

So, $$1-0.8>\left(\dfrac{1}{2}\right)^n$$

or, $$0.2>0.5^n$$

for n = 2, $$0.5^2=0.25$$ which is greater than $$0.2$$

for n = 3, $$0.5^3=0.125$$ which is lesser than 0.2

So, minimum value of n is 3