In a group of 30 students from the foreign language department, 16 students are

Question

In a group of 30 students from the foreign language department, 16 students are taking Spanish. 13 students are taking French, and 11 students are taking Chinese. There are 7 students taking both Spanish and French. 5 students are taking both Spanish and Chinese, and 3 students are taking both French and Chinese. In addition, there is one student taking all three classes. If one of these students is selected at random, determine the probability that: The student is not taking any of the three classes. The student is taking French only. The student is taking one of the three classes. The student is taking all three classes if he or she is taking Spanish. The student not taking French is taking both Spanish and Chinese.

Explanation / Answer

1 TAKING ALL CLASS

7 TAKING SPANISH AND FRENCH , 5 STUDENT TAKING SPANISH AND CHINESE , 3 TAKING CHINESE AND FRENCH.

16 TAKING SPANISH

THEREFORE 16 - 7-5-1 = 3 STUDENTS TAKING ONLY SPANISH

13 TAKING FRENCH

THEREFORE 13 -7-1-3 = 2 ONLY FRENCH

11 TAKING CHINESE

THEREFORE 11 - 3 -1 -5 = 2 TAKING ONLY CHINESE.

A) TOTAL STUDENTS TAKING CLASS = 2+2+3+1+7+5+3 = 23

NOT TAKING ANY CLASS = 30-23 = 7/30

B)AS ABOVE FRNCH>

C)STUDENT TAKING 1 OF THE THREE CLASSES = 2+2+3 = 7/30

D)TAKING ALL CLASSES IF TAKING SPANISH = 1/16

E) STUDENTS TAKING SPAIN AND CHINESE = 3/30

D)

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