In CETT 40 of students identify as industrial Engineering 35

In CETT, 40% of students identify as industrial Engineering, 35% identify as Civil Engineering, and 25% identify as Electrical Engineering. Suppose; 20% Industrial, 60% of Civil, and 30% of Electrical like Football. Suppose a Student from is randomly chosen. Answer the following being sure to clearly identify all event names used: What is the probability that this student like Football? If the student is found a football likes, what is the probability that he is industry Engineering? Suppose the discrete random variable X has probability given by: f(x) = 4 - x / 6, x = 1, 2, 3. Use this information to answer the following: Find the probability that X is at most two?

Solution

(1) Let A be the event that the student from Industrial engineering

      Let B be the event that the student from Civil Engineering

      Let C be the event that the student from Electircal Engineering

      Let D be the event that the student from football

(2) Given P(A)=0.40 P(B)=0.35 P(C)=0.25

                   P(D/A)=0.20   P(D/B)=0.60      P(D/C)=0.30

         probability that student like football

        P(D)=P(D/A)P(A)+P(D/B)P(B)+P(D/C)P(C)

                =(0.20)(0.40)+(0.60)(0.35)+(0.30)(0.25)

                =0.08+0.21+0.075

       P(D) =0.365

(3) P(A/D)=P(D/A)P(A)/P(D)

                =(0.20)(0.40)/0.365

                 =0.08/0.365

          P(A/D) =0.2191