Question

After a genetics experiment on 63 pea plants, the number of plants having certain characteristics was tallied, with the results given to the right. Answer parts (a) through (c). (a) Find the number of plants that were tall and had smooth peas. 23 were tall; 30 had green peas; 42 had smooth peas; 9 were tall and had green peas; 16 had green peas and smooth peas; 3 had all three characteristics; 4 had none of the characteristics. plants

​(a) Find the number of plants that were tall and had smooth peas.

​(b) How many plants were tall and had peas that were neither smooth nor​ green?

​(c) How many plants were not tall but had peas that were smooth and​ green?

Answer 1

Let were tall set of plants be the Sree peas . had Smooth peas n(T) = 23, n(6)= 30, ncs) = 42 n(TNG)=9, ncons) =16 , n(A Tn = 3 nCETnGns]<) = 4 Now, Apply formulae AC AUBUCJ = nCA)+ (B)+ n (€) -ne n( TU GUS) 6)+n (S) - n(TOG)-n (HnS) + -n(TNS) + n(TnSAS) 63-4 = 23+30+42-9 -16 -nCTNs + 3 59 76 -n (TNS) %3D -) n(TnS) = 76 -59 = 07 17 of Plants that were 8tall and had The number Smooth Peas 17 Plants.

Plants were tall but neitner Smootn nor soeen -) n(T) - n (TIS) -nCIOS) + (TOGOS) 23 - 17-9+3 = %3D %3D Were not tall but had peas that were smooth 8 Green = n(son) nC TnSna) = 16 – 3 13 %3D %3D