Question

When an unbiased coin is tossed seven times, what is the probability of obtaining at least 3 tails?

Answer 1

Since the coin is unbiased, probabilities of heads and tails are equal. We denote by $X$ a random variable that corresponds to the number of tails. It has a binomial distribution with parameters 7 and 0.5. The aim is to find the probability $P(X\geq3)$. We have: $P(X\geq3)=1-P(X<3)=1-P(X=0)-P(X=1)-P(X=2)=1-(0.5)^7-C_{7}^1(0.5)^7-C_{7}^2(0.5)^7=1-(0.5)^7-7(0.5)^7-\frac{6\cdot7}{2}(0.5)^7=1-29(0.5)^7=1-29\cdot0.0078125\approx0.773$