Answer:
P(Drive to school | Sophomore) = 0.07 (nearest hundredth)
Step-by-step explanation:
A probability is conditional if it depends on what has already happened.
P(Drive to school | Sophomore) means:
The probability that a student "drives to school" given that they are a "sophomore".
Using the conditional probability formula:
P(B | A) = P(B ∩ A) ÷ P(A)
⇒ P(Drive to school | Sophomore) = P(Drive to school ∩ Sophomore) ÷ P(Sophomore)
Reading from the two-way table, there are 2 people that drive to school AND are a sophomore.
Adding all the values in the table gives us the total number of students: 2 + 13 + 25 + 25 + 20 + 5 + 3 + 2 + 5 = 100
⇒ P(Drive to school ∩ Sophomore) = 2/100 = 0.02
Adding all the values in the sophomore line of the table gives us the total number of sophomores: 2 + 25 + 5 = 30
⇒ P(Sophomore) = 30/100 = 0.3
Now plug these values into the formula:
P(Drive to school | Sophomore) = P(Drive to school ∩ Sophomore) ÷ P(Sophomore)
P(Drive to school | Sophomore) = 0.02 ÷ 0.3
= 1/15
= 0.07 (nearest hundredth)
