Get rich Refer to Exercise 63.

(a) Find P(“a good chance” | female).

(b) Find P(“a good chance”).

(c) Use your answers to (a) and (b) to determine whether the events “a good chance” and “female” are

independent. Explain your reasoning.

In a recent year, the members of the United States Senate were described thus, according to the two-way table:

Consider the following events: D is a democrat, and F is a woman.

The number of favorable outcomes divided by the total number of possible outcomes equals probability. As a result, the following is a definition of condition probability: $P\left(A\right|B)=\frac{P(AandB)}{P\left(B\right)}$

The person in issue is female, according to the inquiry. Now we must calculate the likelihood that the result for "a good chance" is correct.

Therefore,

$P(agoodchanceandFemale)=\frac{favorableoutcomes}{possibleoutcomes}=\frac{663}{4826}$

$P\left(Female\right)=\frac{favorableoutcomes}{possibleoutcomes}=\frac{2357}{4826}$

As a result, the conditional probability is:

$$\begin{gathered} P(agoodchanceFemale)=\frac{P(agoodchanceandFemale)}{P\left(Male\right)} \\ P(agoodchanceFemale)=\frac{663}{2357}\approx 0.2813 \end{gathered}$$

As a result, the likelihood that the result for "a good chance" is

$P(agoodchance/Female)=0.2813$

The goal is to determine the probability that the result for "a good chance" is correct. Therefore, $$\begin{gathered} P(agoodchance)=\frac{favorableoutcomes}{possibleoutcomes} \\ P(agoodchance)=\frac{1421}{4826} \\ P(agoodchance)\approx 0.2944 \end{gathered}$$

part (a) and part (b) , $P(agoodchance/Female)=\frac{663}{2357}\approx 0.2813$

$P(agoodchance)=\frac{1421}{4826}\approx 0.2944$

They should have the same probability, hence they are independent.