Most people love to invest their money A recent survey of 50 people revealed that 22 invested in stocks;25 - Maths - Sets

Question

Most people love to invest their money A recent survey of 50 people
revealed that 22 invested in stocks;25 invested in bonds;39
invested in certificates of deposit; 9 invested in stocks and bonds
;20 invested in bonds and certificates of deposit;6 invested in all
the three;4 had invested in none of them
i) Draw a Venn diagram
ii) Find the number of people who invested in stocks and
certificates of deposit
iii) How many people invested in bonds and in certificates of
deposit, but not in stocks?

Neha Sethi · Accepted Answer

Dear student

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Let S,B and D represents set of people who had invested in stocks,bonds,certificates of deposits respectively
n(S)=a+b+d+en(B)=b+c+e+fn(D)=d+e+f+gn(S∩B)=b+en(B∩D)=e+fn(S∩D)=d+en(S∩B∩D)=eIt is given thatn(S'∩B'∩D')=4⇒n(U)-nS∪B∪D=4⇒nS∪B∪D=50-4=46Also,givenn(S)=22n(B)=25n(D)=39n(S∩B)=9n(B∩D)=20n(S∩B∩D)=62) n(S∩D)=n(S)+n(B)+n(D)-n(S∩B)-n(B∩D)+n(S∩B∩D)-nS∪B∪D=22+25+39-9-20+6-46=173) nB∩D∩S'=n(B∩D)-n(S∩B∩D)=20-6=14