4. the table shows the probabilities of a response chocolate or vanilla when asking a child or adult. use the formula for conditional probability to determine independence. chocolate | vanilla | total adults 0.21 0.39 0.60 children 0.14 0.26 0.40 total 0.35 0.65 1.00 a. are the events “chocolate” and “adults” independent? why or why not? b. are the events “children” and “chocolate” independent? why or why not? c. are the events “vanilla” and “children” independent? why or why not?

All events are independent

Step-by-step explanation:

You are given the table

Two events A and B are independent when

a) A="Chocolate"

B="Adults"

A and B="Chocolate and Adults"

Since events are independent

b) A="Children"

B="Chocolate"

A and B="Children and Chocolate"

Since events are independent

c) A="Vanilla"

B="Children"

A and B="Vanilla and Children"

Since events are independent

answer for #1 is c

answer for #2 is d

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step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)