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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
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