Question

Use the table to answer the question.

Circle and Triangle Categorized into Different Colors
Color
Shape Red Yellow TOTAL
Circle 12 18 30
Triangle 20 30 50
Total 32 48 80
If event A
is that a shape is a triangle and event B
is that a shape is yellow, are the two events independent? Explain.

(1 point)
Responses

No, because both events do not include triangles.
No, because both events do not include triangles.

No, because both events do not include yellow.
No, because both events do not include yellow.

Yes, because P(A)=P(B)
.
Yes, because upper P left parenthesis upper A right parenthesis equals upper P left parenthesis upper B right parenthesis .

Yes, because P(A|B)=P(A)
.

Answer 1

Yes. P(A) = 50/80 = 0.625, P(B) = 48/80 = 0.6, and P(A ∩ B) = 30/80 = 0.375. Since P(A)P(B) = 0.625·0.6 = 0.375 = P(A ∩ B), the events are independent. Equivalently P(A|B) = 0.375/0.6 = 0.625 = P(A).