Answer: The probability the student studies Art and Biology is 0.2143. Step-by-step explanation: Denote the events as follows: A = a students studies Art B= a students studies Biology The information provided is: N = 42 n (An B) = 9 n (A' n B) = 10 n (A' n B') =7 Then the number of students who study Art but not Biology is: n(An B') = N -n (An B) -n (A' nB) - n (A'n B') = 42 - 10 - 7 - 9 = 16 The number of students who study Art but not Biology is 16. Compute the probability the student studies Art and Biology as follows: P(ANB) n(ANB) = 0.2143 Thus, the probability the student studies Art and Biology is 0.2143.
