數學PP 1題求助解釋

chasechase12

of the students who eat in a certain cafa, each student either likes or dislikes A, and each student likes or dislikes B, of these students, 2/3 dislike A, and of those who dislike A, 3/5 also dislike B, How many of the students like B but dislike A.

1. 120 students eat in the cafa.

2. 40 students like A.

ans: D

sdcar2010

Conditions 1 and 2 are basically the same thing: (1 - 2/3) x 120 = 40  So we know that 80 students dislike A.  Since among the student who dislike A, 3/5 also dislike B, we know 2/5 of the same group likes B.  Therefore the answer for the number of students like b but dislike A = 80 x 2/5 = 32

chasechase12

TKS~!