How do you make a tree diagram for this? (and in general)
1) of the voters in a certain city, 40% are republicans and 60% are democrats. among the republicans, 70% are in favor of a particular bond issue whereas 80% of the democrats favor the issue. if a voter is selected at random in the city, what is the probability that he or she will favor the bond issue?
can someone check this answer i got. i got 37/250.
two branches are republican and democrat.
from republican two branches are favor and dislike. probability of being republican 40/100 and probability of favoring issue is 70/100 and disliking is 30/100
from democrat two branches are favor and dislike. probability of being democrat is 60/100. probability of favoring issue is 80/100 and disliking is 20/100.
Math:
P(Republican and favor)=40/100 x 70/100 = 280/10000 = 7/250
P(Democrat and favor)=60/100 x 20/100 = 1200/10000 = 3/25
Favor= P(Rep. and favor) + P(Dem. and favor)
7/250 + 3/25 = 37/250
To create a tree diagram for this problem, we need to break it down into its components and account for all the possible outcomes.
Step 1: Start by drawing a vertical line or stem labeled "Voter" at the top of your diagram.
Step 2: Split the stem into two branches representing the political parties: Republicans and Democrats. Assign the probabilities for each party on these branches: 40% for Republicans and 60% for Democrats.
Step 3: Next, draw branches coming from the Republican branch representing the two possibilities: in favor of the bond issue and not in favor of the bond issue. Assign the corresponding probabilities: 70% for in favor and 30% for not in favor.
Step 4: Similarly, draw branches from the Democrat branch representing the two possibilities: in favor of the bond issue and not in favor of the bond issue. Assign the probabilities: 80% for in favor and 20% for not in favor.
Now, your tree diagram should have four branches at the bottom, representing all the possible outcomes: Republican and in favor, Republican and not in favor, Democrat and in favor, Democrat and not in favor.
To calculate the probability of a voter favoring the bond issue, we need to consider all the paths that lead to that outcome. In this case, we need to add up the probabilities of the two paths that indicate being in favor: (40% x 70%) + (60% x 80%).
Therefore, the probability that a randomly selected voter in the city favors the bond issue is calculated as follows:
0.4 x 0.7 + 0.6 x 0.8 = 0.28 + 0.48 = 0.76 or 76%.
So, there is a 76% probability that a randomly selected voter in the city will favor the bond issue.