In a large high school 15% of sophomores, 25% of Juniors, and 55% of seniors drive to school. According to the registration office, 24% of students are sophomores, 26% are juniors, and 30% are seniors. Suppose we select one student from this school at random and record which class they are in as well as whether they drive to school or not

The tree diagram that models this random process is shown in the image below and the probability that the student drives to school is 0.3325

The objective of the information given in the question is to draw a tree diagram that models this random process and to find the probability of the student that drove to school.

From the image attached below, we can see the tree diagram that models the random process.

The probability of student that drives to school can be computed by using the formula:

[tex]\mathbf{P(Drive) = \dfrac{(P(S|D)\times P(S)) +( P(J|D) \times P(J) ) + (P(Se|D) \times {(Se)} }{P(S+J+ Se) }}[/tex]

[tex]\mathbf{P(Drive) = \dfrac{(15\% \times 24\%) +( 25\%\times 26\%) + (55\%\times30\%)} {(24\%+ 26\%+ 30\%) }}[/tex]

[tex]\mathbf{P(Drive) = \dfrac{(36) +( 65) + (165)} {(8) }}[/tex]

P(Drive) = 0.3325

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