Question

Question Help A survey of 500 farmers showed that of the farmers, 125 grew only wheat, 111 grew only corn, 93 grew only oats, 197 grew wheat, 54 grew wheat and com, 51 grew wheat and oats, and 178 grew corn. Determine the number of farmers who a) grew at least one of the three, b) grew all three, c) did not grow any of the three, and d), grew exactly two of the three. a) of the farmers, grew at least one of the three crops. (Simplify your answer.)

Answer 1

In the ans. Int. Of all W,C,O is the ans. Of part b i.e. 33 and 414 of part a, 86 of part c and 51 of part d. Thank you!
Total no. of farmers (A UBUC) = 500 . . grew Wan(w),197 " Canc): 178 W&C : nc wnc)=54 W&o= newnol = 51 " W W onlyn (w*) = 125 Conly = ncc*)= 111 O only = nCor)= 93. & we know that nCA UBUC) n(A) + n08 +ncc) - En (ANB) + DC Alloc So, first we will find the missing terms. ll. 1. nCAMBno) - We know nCA*) n(A) - [NCANB) +n (ANC) - n(Allele (Wx) = n(w) -[n (WN c) + (w/o)-(whotos] ) 125 = 197 -[ 54+ 51 - n (W210)] => Iniwnicno) = 33 similarly | P( c*), (c)-( ( (c) ( 1c) - h (w/12/ 17 01 - 178-[54 + n conc) - 33] & Inconc) = 46 & n10*) -93=n (0) -[ 46+51-33] In(o) = 157] Now, we have all the entries, so SUS C E VITWA

by eah .cs - NCAUBUC) = n(A) who don't putting all the values- ENCANB) + CAMBNC) & no. of participate 2 500 - 197+ 178 + 157 - 54-51-46+33+ no of who don't grew any three, 500 = 414 + n(u) They, who don't grew any = 86)

Total a Now, They who grow at least 1 - who don't grew any of 3- a 500- 86 = 1414

on so. two Now, Those who grew exactly - (ANB) - CAMBNC) , fom wd c- 54 - 33 = 21 w & o - 51-33 = 18 45-33= 12

for So, = - w & c- total non of, who grew exactly 21+18 + 12 3. 51 two ~