Answer:
a) Yes the events Chocolate and Adults are independent
b) Yes the events Children and Chocolate are independent
c) Yes the events Vanilla and Children are independent
Step-by-step explanation:
* Lets study the meaning independent and dependent probability Ā
- Two events are independent if the result of the second event is not
Ā affected by the result of the first event
- If A and B are independent events, the probability of both events Ā
Ā is the product of the probabilities of the both events
- P (A and B) = P(A) Ā· P(B)
* Lets solve the question
# From the table: Ā
- The probability of chocolate is 0.35
- The probability of vanilla is 0.65
- The probability of adults is 0.60
- The probability of children is 0.40
- The probability of chocolate and adults is 0.21
- The probability of chocolate and children is 0.14
- The probability of vanilla and adult is 0.39
- The probability of vanilla and children is 0.26
a.
āµ P(chocolate) = 0.35
āµ P(Adults) = 0.60
āµ Two events are independent if P (A and B) = P(A) Ā· P(B) Ā
āµ P(chocolate) Ā· P(adults) = (0.35)(0.60) = 0.21
āµ P(chocolate and adults) = 0.21
ā“ P(chocolate and adults) = P(chocolate) Ā· P(adults)
ā“ The events chocolate and adults are independent
b.
āµ P(chocolate) = 0.35
āµ P(children) = 0.40
āµ Two events are independent if P (A and B) = P(A) Ā· P(B) Ā
āµ P(chocolate) Ā· P(children) = (0.35)(0.40) = 0.14
āµ P(children and chocolate) = 0.14
ā“ P(chocolate and children) = P(chocolate) Ā· P(children)
ā“ The events chocolate and children are independent
c.
āµ P(vanilla) = 0.65
āµ P(children) = 0.40
āµ Two events are independent if P (A and B) = P(A) Ā· P(B) Ā
āµ P(vanilla) Ā· P(children) = (0.65)(0.40) = 0.26
āµ P(vanilla and children) = 0.26
ā“ P(vanilla and children) = P(vanilla) Ā· P(children)
ā“ The events vanilla and children are independent
