I'm confused about some simple binomial distribution problems in my textbook. Suppose p = 0.2 and n = 4. Calculate:

• P(x=2). The answer I got was 0.512
• P(x<=2). The answer I got was 1.536

I am using the standard binomial formula. The textbook is giving me different answers however, even though I followed the formula to the letter. The textbook answers are 0.5136 and 0.9728 respectively.

$P(x=k) = \binom{n}{k} p^k\cdot q^{n-k}, n = 4, p = 0.2, q = 0.8, x = 2 \Rightarrow P(x=2) = \binom{4}{2} 0.2^2\cdot 0.8^2=....$, and $P(x \leq 2) = P(x=0)+P(x=1)+P(x=2)$.