At a school, the probability that a student takes Technology and Spanish is 0.087. The probability that a student takes Technology is 0.68. What is the probability that a student takes Spanish given that the student is taking Technology?
Question
At a school, the probability that a student takes Technology and Spanish is 0.087. The probability that a student takes Technology is 0.68. What is the probability that a student takes Spanish given that the student is taking Technology?
Solution
To solve this problem, we need to use the formula for conditional probability, which is:
P(A|B) = P(A ∩ B) / P(B)
In this case, we want to find the probability that a student takes Spanish given that the student is taking Technology. So, Spanish is event A and Technology is event B.
From the problem, we know that:
P(A ∩ B) = P(Technology and Spanish) = 0.087 P(B) = P(Technology) = 0.68
Substituting these values into the formula, we get:
P(A|B) = P(Spanish|Technology) = P(Technology and Spanish) / P(Technology) = 0.087 / 0.68 = 0.128 (rounded to three decimal places)
So, the probability that a student takes Spanish given that the student is taking Technology is approximately 0.128 or 12.8%.
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