Question

When an unbiased coin is tossed seven times, what is the probability of obtaining at least 4 heads?

Answer 1

Let $X=$ the number of heads: $X\sim Bin(n, p)$

Given $n=7, p=0.5$

$$P(X\geq4)=P(X=4)+P(X=5)$$

$$+P(X=6)+P(X=7)$$

$$=\dbinom{7}{4}(0.5)^4(1-0.5)^{7-4}+\dbinom{7}{5}(0.5)^5(1-0.5)^{7-5}$$

$$+\dbinom{7}{6}(0.5)^6(1-0.5)^{7-6}+\dbinom{7}{7}(0.5)^7(1-0.5)^{7-7}$$

$$=\dfrac{1}{128}(35+21+7+1)=0.5$$

The probability of obtaining at least 4 heads is 0.5.