Sampling senators Refer to Exercise 50.

(a) Construct a Venn diagram that models the chance process using events R: is a Republican, and F: is female.

(b) Find $P(R\cup F)$ Interpret this value in context.

(c) Find $P(R^c\cap F^c)$ Interpret this value in context.

The two-way table below shows who was a member of the United States Senate in the previous year.

A Venn diagram is a visual representation of relationships between things or limited groups of objects using circles. Circles that overlap have similar qualities to circles that do not overlap. Venn diagrams are graphic representations of the similarities and differences between two concepts.

The model is based on a random process with the events R: Republican and F: Female.

The Venn diagram is transformed into,

$Probability=\frac{Numberoffavorableoutcomes}{Totalpossibleoutcomes}$

Total number of possible outcomes: $100$

Therefore, $P(R\cup F)=\frac{36+4+13}{100}=0.53$

$P\left(A^c\right)=1-P\left(A\right)$

$100$ different scenarios are possible.

Therefore,

The two-way table below shows who was a member of the United States Senate in the previous year.

A Venn diagram is a visual representation of relationships between things or limited groups of objects using circles. Circles that overlap have similar qualities to circles that do not overlap. Venn diagrams are graphic representations of the similarities and differences between two concepts.

The model is based on a random process in which event B: Eats breakfast on a regular basis and M: is male.

Venn diagram becomes,

Probability =Number of favorable outcomes/Total possible outcomes

The total number of conceivable outcomes is 100

Therefore, P(R ∪ F) = = 0.53

P(Ac)=1-P(A)

100 different scenarios are possible.

Therefore,

P(R ∩ ) = 1 − P(R ∪ F) c Fc

P(R ∩ ) = 1 − 0.53 = 0.47