Question

A survey is made in a neighborhood of 80 voters. 65 are democrats and 15 are republicans. of the democrats, 35 are women, while 5 of the republicans are women. if one subject from the group is randomly selected, find the probability the individual is a democrat or a republican.

Answer 1

Answer:  1

Step-by-step explanation:

Given: Total voters n(S)= 80

Number of democrats n(D)= 65

Number of republicans n(R)= 15

Number of voters that are democrats and republicans=$n(D\cap R)=0$

[Since both are different parties and thus independent means no individual can be common in both parties]

Then, the number of individuals that are  democrat or republican is given by :-

$n(D\cup R)=n(D)+n(R)-n(D\cap R)\\\\\Rightarrow n(D\cup R)=65+15-0\\\\\Rightarrow n(D\cup R)=80$

If one subject from the group is randomly selected, find the probability the individual is a democrat or a republican=$P(D\cup R)=\frac{n(D\cup R)}{n(S)}=\frac{80}{80}=1$

Answer 2

Total voters=v=80
total no. of democrats=d=65
total no. of republicans=r=15
probability of democrats=p1=65/80=0.8125
probability of republicans=p2=15/80=0.1875
probability of a democrat or a republican=p1+p2=0.8125+0.1875=1 <span />