After a genetics experiment on 61 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.

nothing plants

22

were tall;

30

had green peas;

34

had smooth peas;

8

were tall and had green peas;

16

had green peas and smooth peas;

3

had all three characteristics;

6

had none of the characteristics.

Number of trees which are tall and have smooth peas are 4

Explanation:

The easiest way to explain this problem is by using venn diagram that is attached to my answer.

Now let's start with explanations.

1. Both tall, green peas and smooth peas trees = 3. So, put it in the middle, at the intercection of all three circles.

2. Both Tall and Green peas trees = 8. So put it at the intersection of T and G circles.

3. Both Green peas and Smooth peas trees = 16. Put it at the intersection of G and S.

4. Let's assume that both Tall and Smooth peas trees amount to X (for calculation purposes). Locate it at the intersection of T and S. This X is what we need to identify.

5. Totally Tall trees amount to 22. This means that in the remaining region we can locate such equation as 22 - 8 - 3 - X = 11 - X

6. Totally Green peas trees amount to 30. So, remaing area will be equal to 30 - 8 - 3 - 16 = 3

7. Totally Smooth peas trees amount to 34. Remaining area is 34 - X -3 -16 = 15 - X.

8. Now we can add up all our calculated numbers and equations and equate it to overall number of trees, 61.

* Also, we have 6 trees which have none of the charecteristics.

So,

61 = (11-x)+8+3+x+3+16+(15-x) + 6

x=1

The intersection of T and S is x+3 ⇒ 1+3=4

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