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 freshman, sophomores, juniors and seniors, the portion of the students who live in the dormitory are respectively 80%, 60%,30% and 20%. What is the probability that a randomly selected student is a sophomore who does not live in a dormitory? Show your answer is obtained.
P(soph) = .25
P(non dorm soph) = (1-.60)
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
To find the probability that a randomly selected student is a sophomore who does not live in a dormitory, we need to multiply the probability of being a sophomore with the probability of not living in a dormitory as a sophomore.
First, let's calculate the probability of being a sophomore. According to the information given, 25% of the students are sophomores.
P(sophomore) = 0.25
Next, let's calculate the probability of not living in a dormitory as a sophomore. According to the information given, 60% of sophomores live in a dormitory. Therefore, the probability of not living in a dormitory as a sophomore is:
P(not living in a dormitory as a sophomore) = 1 - P(living in a dormitory as a sophomore)
= 1 - 0.60
= 0.40
Now, we can calculate the probability of a randomly selected student being a sophomore who does not live in a dormitory by multiplying the two probabilities:
P(sophomore and not living in a dormitory) = P(sophomore) * P(not living in a dormitory as a sophomore)
= 0.25 * 0.40
= 0.10
Therefore, the probability that a randomly selected student is a sophomore who does not live in a dormitory is 0.10, or 10%.