In a history class, the probability of earning an A is .7 times the probability of earning a B, and the probability of earning a C is 1.4 times the probability of earning a B. Assuming that all grades are A, B, or C, how many B's will there be in a history class of 31 students?
+23251 Let the number of students who earn a 'B' is B.
Since the probability of earning an 'A' is 0.7 times the probability of earning a 'B', the number of A's earned will be 0.7·B.
Since the probability of earning a 'C' is 1.4 times the probability of earning a 'B', the number of C's earned will be 1.4·B.
Since there is a total of 31 students: 0.7B + B + 1.4B = 31
---> 3.1B = 31
---> B = 10 (10 students will earn a 'B'.)
Number of A's: 0.7B = 0.7·10 = 7 (7 students will earn an 'A'.)
Number of C's: 1.4B = 1.4 ·10 = 14 (14 students will earn a 'C'.)
