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
Explanation:
* Lets study the meaning independent and dependent probability
- Two events are independent if the result of the second event is not
affected by the result of the first event
- If A and B are independent events, the probability of both events
is the product of the probabilities of the both events
- P (A and B) = P(A) · P(B)
* Lets solve the question
# From the table:
- 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.
∵ P(chocolate) = 0.35
∵ P(Adults) = 0.60
∵ Two events are independent if P (A and B) = P(A) · P(B)
∵ P(chocolate) · P(adults) = (0.35)(0.60) = 0.21
∵ P(chocolate and adults) = 0.21
∴ P(chocolate and adults) = P(chocolate) · P(adults)
∴ The events chocolate and adults are independent
b.
∵ P(chocolate) = 0.35
∵ P(children) = 0.40
∵ Two events are independent if P (A and B) = P(A) · P(B)
∵ P(chocolate) · P(children) = (0.35)(0.40) = 0.14
∵ P(children and chocolate) = 0.14
∴ P(chocolate and children) = P(chocolate) · P(children)
∴ The events chocolate and children are independent
c.
∵ P(vanilla) = 0.65
∵ P(children) = 0.40
∵ Two events are independent if P (A and B) = P(A) · P(B)
∵ P(vanilla) · P(children) = (0.65)(0.40) = 0.26
∵ P(vanilla and children) = 0.26
∴ P(vanilla and children) = P(vanilla) · P(children)
∴ The events vanilla and children are independent