At the Faculty of Computing, 53% of the

To solve the problem, we are given that 53% of the students are male and 47% are female at the Faculty of Computing. Additionally, 35% of the males and 20% of the females major in Computer Networking. We need to find the probability that a student selected at random from this group is majoring in Computer Networking.
Let's denote the event of a student being male as $M$ and the event of a student being female as $F$. The probability of a student being male is $P(M)=0.53$, and the probability of a student being female is $P(F)=0.47$.
We are also given that 35% of the males major in Computer Networking. Therefore, the probability of a male student majoring in Computer Networking, denoted as $P(CN|M)$, is $0.35$.
Similarly, 20% of the females major in Computer Networking. Therefore, the probability of a female student majoring in Computer Networking, denoted as $P(CN|F)$, is $0.20$.
To find the probability that a student selected at random from this group is majoring in Computer Networking, we can use the law of total probability. This law states that the probability of an event can be expressed as the sum of the probabilities of that event occurring under each mutually exclusive condition.
Using the law of total probability, the probability of a student majoring in Computer Networking, denoted as $P(CN)$, can be calculated as:
$P(CN)=P(CN|M)·P(M)+P(CN|F)·P(F)$
Substituting the given values, we have:
$P(CN)=0.35·0.53+0.20·0.47$
Calculating this expression gives:
$P(CN)\approx 0.1855$
Therefore, the probability that a student selected at random from this group is majoring in Computer Networking is approximately 0.1855.