According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What is the probability that it is a Junior or a senior?
What formula would I use for this?
total junior or seniors / total students
(.16+.24)/1.00 = .40
Those who live in the dorm:
(.16*.30 + .24*.20)/1.00 = .096
To calculate the probability that a student is either a junior or a senior, you can add the probabilities of these two events occurring separately.
The formula for calculating the probability of one event or another (A or B) is:
P(A or B) = P(A) + P(B) - P(A and B)
In this case, you want to find the probability that a student is either a junior or a senior. Let's assign the following probabilities:
P(J) = Probability of being a junior = 16%
P(S) = Probability of being a senior = 100% - P(F) - P(So) - P(J) = 100% - (35% + 25% + 16%)
Now you can plug these values into the formula:
P(J or S) = P(J) + P(S) - P(J and S)
Since the question does not provide the probability of juniors being seniors, we assume they are mutually exclusive. Therefore, the probability of a student being a junior and a senior at the same time (P(J and S)) is 0.
Simplifying the formula:
P(J or S) = P(J) + P(S)
P(J or S) = 16% + (100% - (35% + 25% + 16%))
Finally, calculate the sum:
P(J or S) = 16% + 24% = 40%
Therefore, the probability that a student is either a junior or a senior is 40%.
To find the probability that a student is either a junior or a senior, you can use the concept of complementary events. The probability of an event occurring is equal to 1 minus the probability of the event not occurring.
In this case, we know that the percentage of junior students is 16% and senior students make up the remaining percentage. To calculate the probability of a student being either a junior or a senior, you need to find the complement of the probability of the student being a freshman or a sophomore.
First, calculate the complement of the probability that a student is a freshman or a sophomore:
1 - (probability of being a freshman + probability of being a sophomore)
Next, find the probability of being a freshman or a sophomore:
probability of being a freshman + probability of being a sophomore
Using the information provided, plug in the values into the formula:
1 - [(percentage of freshmen + percentage of sophomores) / 100]
1 - [(35% + 25%) / 100]
1 - [60% / 100]
1 - 0.60
The probability that a student is a junior or a senior is 0.40 or 40%.
In summary, the formula used is:
Probability (junior or senior) = 1 - (Probability (freshman or sophomore))