In a class of 50 students, 29 are Democrats, 11 are business majors, and 5 of the business majors are Democrats. If one student is randomly selected from the class, find the probability of choosing: (a) Democrat who is not a business major. (b) A student who is neither a Democrat nor a business major.
a. 11/25 b. 4/10
a. 12/25 b. 3/10
a. 9/25 b. 6/10
a. 7/25 b. 5/10
best done with a Venn diagram.
Two intersecting circles, one for Democrat, the other for Business major
enter 5 in the intersection of the two circles
enter 29-5 or 24 in the "Democrat only" part of the Venn
enter 11-5 or 6 in the business only part
in the circles you now have 24 + 5 + 6 or 35 entered.
Where do the remainders of the total of 50 go ??
You now know where everybody fits in, and should be able
to answer your question
too this user
if you ever search this and find this message
do you play roblox or minecraft
Solve the following equation. Determine whether the equation is an identity, conditional equation, or an inconsistent equation: 3 - 5(2x + 1) - 2(x - 4) = 0
To find the probability, we need to calculate the ratio of the number of favorable outcomes to the total number of outcomes.
Given information:
Total number of students in the class = 50.
Number of Democrats = 29.
Number of business majors = 11.
Number of business majors who are Democrats = 5.
Now let's solve each part of the question:
(a) Probability of choosing a Democrat who is not a business major:
Number of Democrats who are not business majors = Number of Democrats - Number of business majors who are Democrats = 29 - 5 = 24.
Total number of students who are not business majors = Total number of students - Number of business majors = 50 - 11 = 39.
Therefore, the probability of choosing a Democrat who is not a business major is:
P(Democrat and not business major) = Number of Democrats who are not business majors / Total number of students who are not business majors = 24 / 39 = 8/13.
(b) Probability of choosing a student who is neither a Democrat nor a business major:
Number of students who are neither Democrats nor business majors = Total number of students - Number of Democrats - Number of business majors + Number of business majors who are Democrats = 50 - 29 - 11 + 5 = 15.
Total number of students = 50.
Therefore, the probability of choosing a student who is neither a Democrat nor a business major is:
P(not Democrat and not business major) = Number of students who are neither Democrats nor business majors / Total number of students = 15 / 50 = 3/10.
So, the correct answers are:
(a) Probability of choosing a Democrat who is not a business major = 8/13.
(b) Probability of choosing a student who is neither a Democrat nor a business major = 3/10.