The following table summarizes the availability of trucks with air bags and bucket seats at a dealership. Bucket seats No Bucket Seats Total Air Bags 75 50 125 No Air Bags 35 60 95 Total 110 110 220 What is the probability of randomly selecting a truck with air bags and bucket seats? A) 0.16. B) 0.28. C) 0.57. D) 0.34. So the correct answer is D) 0.34. 75 / 220 = 0.34. I understand the simple solution is the one above, But how come you can’t calculate P(it has air bags) = 125/220 = 0.5682 P(it has bucket seats) = 110/220 = 0.5 So therefore P(it has airbags and it has bucket seats) = 0.5682 * 0.5 = 0.28 ?
But they aren’t independent and your calculation says they are…
i see what you’re saying Joey, but why are having airbags and bucket seats dependent on each other? why aren’t they independent?
do u mean to say if a truck has airbags, it cannot have bucket seats – this is what independent means – independent is in the meaning of “events”.
Ah, ok I see my mistake. Thanks for your help.
cpk123 Wrote: ------------------------------------------------------- > do u mean to say if a truck has airbags, it cannot > have bucket seats – this is what independent > means – independent is in the meaning of > “events”. Yikes - That’s “mutually exclusive”. Independent means the probability of one event happening is not influenced by another event happening. So here it means that P(Bucket Seat | Airbag) = P(Bucket Seat) (and flipped)
yikes! thanks joey
Just to add on Joe post. When two Events A and B are dependent: P(A and B)= P(A/B) x P(B) (I) When two events A and B are independent: P(A and B)=P(A) x P(B) (II) In the case your presented, the two events are dependent so if you compute it as: P(it has airbags and it has bucket seats) = 0.5682 * 0.5 = 0.28 you would be assuming that, P(it has airbags knowing it has bucket seats)=P(it has airbags) which is not true as the two events are dependent. Now for your question to why they are dependent and not independent: The answer is when one of those event occur, it give more information about the second event . For Example if you know that the truck has airbag the probabilty of selecting a truck with a bucket seat is: P(A)= Number of favorable case/ number of possibe case= 75/125 Now if you you don’t know whether or not the truck has an Airbag P(A)=75/220 So you see that Knowing that the truck has an airbag increase your chance of selecting a truck with airbag and bucket seat. Now if the two event were independent knowing that the truck as an airbag or not, would not have increase you chance of selecting a truck with airbag and bucket seat. They would have not information given about the second event To summarize, two event are independent when the occurence of one give more information about the other. And they are independent when the occruence of one does not give you any information about the other.
Giristide your final sentence “To summarize, two event are independent when the occurence of one give more information about the other. And they are independent when the occruence of one does not give you any information about the other.” did you actually mean to say “To summarize, two event are dependent when the occurence of one give more information about the other. And they are independent when the occruence of one does not give you any information about the other.”
Yes that’s what I meant to say, sorry for the confusion.
no worries, thanks for your help.