Question

Connor flips a coin four times. if he can assume that heads occurs 50% of the time and tails occurs 50% of the time, what is the probability of at most 2 heads appearing?

Answer 1

The probability is 0.6875.

We find the probability of 0 heads, 1 heads, and 2 heads:

$_4C_0(0.5)^0(0.5)^4+_4C_1(0.5)^1(0.5)^3+_4C_2(0.5)^2(0.5)^2 \\ \\=\frac{4!}{4!0!}(0.5)^4+\frac{4!}{1!3!}(0.5)(0.5)^3+\frac{4!}{2!2!}(0.5)^2(0.5)^2 \\ \\=0.5^4+4(0.5)^4+6(0.5)^4=0.6875$