We are asked to calculate $P(x \le 3)$ for the binomial random variable $x$ with $n = 4$ and $p = 0.70$. Since the binomial distribution is a discrete probability distribution, we can calculate $P(x \le 3)$ by adding $p(0)$, $p(1)$, $p(2)$, and $p(3)$. In part (a) we found
$p(3) = 0.4116$. To find the other three needed probabilities, we can use the probability formula for the binomial distribution.
$p(x) = P(x \text{ successes among the } n \text{ trials}) = \frac{n!}{x!(n-x)!}p^x(1-p)^{n-x}$
$p(0) = \frac{4!}{0!(4-0)!} \times (1-0.70)^{4-0}$
$p(1) = \frac{4!}{1!(4-1)!}(0.70)^1(1-0.70)^{4-1}$
$p(2) = \frac{4!}{2!(4-2)!}(0.70)^2(1- \text{_____})^{4-2}$
