Question

in a political science class of 50 students, 20 favor abolishing the electoral college (A) and thus electing the president of the United states by popular vote. If 2 students are selected at random from this class, what is the probability that both of them favor abolition of the electoral college? Draw a tree diagram. ​

Answer 1

Answer:

The probability that both the students selected favor abolishing the electoral college is 0.16.

Step-by-step explanation:

Let X = number of students who favor abolishing the electoral college.

Of the 50 students 20 favor abolishing the electoral college.

The probability of X is, $P(X)=\frac{20}{50} =0.40$.

The random variable X follows a Binomial distribution with parameters n = 2 and p = 0.40.

The probability function of Binomial distribution is:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,...$

Compute the probability that both the students selected favor abolishing the electoral college as follows:

$P(X=2)={2\choose 2}(0.40)^{2}(1-0.40)^{2-2}=0.16$

Thus, the probability that both the students selected favor abolishing the electoral college is 0.16.