Question

1. compute the probability of x successes, using table b in appendix a.

a. n = 2, p = 0.30, x = 1
b. n = 4, p = 0.60, x = 3

Explanation:

Step1: Recall binomial probability formula

The binomial probability formula is $P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}$, where $C(n,k)=\frac{n!}{k!(n - k)!}$. But we are asked to use Table - B. In the binomial probability table, we look up the values based on $n$, $p$, and $X$.

Step2: For part a

For $n = 2$, $p=0.30$, and $X = 1$. Looking up in the binomial probability table (Table - B), we find the value corresponding to $n = 2$, $p = 0.30$, and $X = 1$. The binomial coefficient $C(2,1)=\frac{2!}{1!(2 - 1)!}=\frac{2!}{1!1!}=2$. Then $P(X = 1)=C(2,1)\times0.3^{1}\times(1 - 0.3)^{2 - 1}=2\times0.3\times0.7 = 0.42$. Using the table, we can directly read the value.

Step3: For part b

For $n = 4$, $p = 0.60$, and $X = 3$. The binomial coefficient $C(4,3)=\frac{4!}{3!(4 - 3)!}=\frac{4!}{3!1!}=4$. Then $P(X = 3)=C(4,3)\times0.6^{3}\times(1 - 0.6)^{4 - 3}=4\times0.216\times0.4=0.3456$. Using the table, we directly read the value.

Answer:

a. $0.42$
b. $0.3456$