Answer to Question #205134 in Statistics and Probability for Shema Derrick

Question

At Kennedy Middle 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?

Answer 1

$At\space Kennedy\space Middle\space School,\space the\space probability\space that\space a\space student\space takes\space Technology\space and\space Spanish\space is\space 0.087.\\ \space The\space probability\space that\space a\space student\space takes\space Technology\space is\space 0.68.\\ \space What\space is\space the\space probability\space that\space a\space student\space takes\space Spanish\space given\space that\space the\space student\space is\space taking\space Technology?\\ --------------------------\\ Solution:\space \\ given\\ the\space probability\space that\space a\space student\space takes\space Technology\space and\space Spanish\space is\space 0.087.\\ \space P(Technology\space and\space Spanish)=0.087\\ The\space probability\space that\space a\space student\space takes\space Technology\space is\space 0.68.\\ P(Technology)=0.68\\ then\space probability\space that\space a\space student\space takes\space Spanish\space given\space that\space the\space student\space is\space taking\space Technology\\ we\space use\space conditonal\space probability\\ P(Spanish|Technology) \space \space =\space \space \frac{P(Technology\space and\space Spanish)}{P(Technology)}\\ \space =\space \space \frac{0.087}{0.68}\\ =\space \space 0.13\\ =13\%\\$