Problem

29.
(a) In this part you may use this Venn diagram to help you answer the questions.
In a class of 30 students, 25 study French (F),18 study Spanush (S) One student does not study French or Spanish.
(i) Find the number of students who study French and Spanish
(ii) One of the 30 students is chosen at random.
Find the probability that this student studies French but not Spanish.
(iii) A student who does not study Spanish is chosen at random.
Find the probability that this student studies Erench

Answer

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Answer

P(F|S¯)=1112

Steps

Step 1 :n(FS)=n(F)+n(S)n(FS)

Step 2 :n(FS)=25+1829

Step 3 :n(FS)=14

Step 4 :n(FS)=n(F)n(FS)

Step 5 :n(FS)=2514

Step 6 :n(FS)=11

Step 7 :P(FS)=n(FS)n(U)

Step 8 :P(FS)=1130

Step 9 :n(S¯)=n(U)n(S)

Step 10 :n(S¯)=3018

Step 11 :n(S¯)=12

Step 12 :P(F|S¯)=n(FS¯)n(S¯)

Step 13 :P(F|S¯)=1112

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