Answer:
Eating dinner and eating dessert are dependent events because
P(dinner) . P(dessert) = 0.9 × 0.6 = 0.54 which is not equal to
P(dinner and desert) = 0.5 ⇒ answer A
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
∵ There is a 90% chance that a person eats dinner
∴ P(eating dinner) = 90/100 = 0.9
∵ There is a 60% chance a person eats dessert
∴ P(eating dessert) = 60/100 = 0.6
- If eating dinner and dating dessert are independent events, then
probability of both events is the product of the probabilities of the
both events
∵ P(eating dinner and dessert) = P(eating dinner) . P(eating dessert)
∴ P(eating dinner and dessert) = 0.9 × 0.6 = 0.54
∵ There is a 50% chance the person will eat dinner and dessert
∴ P(eating dinner and dessert) = 50/100 = 0.5
∵ P(eating dinner and dessert) ≠ P(eating dinner) . P(eating dessert)
∴ Eating dinner and eating dessert are dependent events because
P(dinner) . P(dessert) = 0.9 × 0.6 = 0.54 which is not equal to
P(dinner and desert) = 0.5