# Thread: recycling probability, apply which info.

1. ## recycling probability, apply which info.

there is a study that shoat eightysix percent of people have access to curbside or drop off recycling programs. Suppose there are four people randomly selected.

what is the probability that at least one of the four does not have access to recycling?

and then if none of the four had acces to recycling, is there evidence to suggest the claim is not correct?

.........

i know there are eighty six percent of everyone who recycle, i'm getting confused as to what information is relevant to find each question.

2. Hello rcmango
Originally Posted by rcmango
there is a study that shoat eightysix percent of people have access to curbside or drop off recycling programs. Suppose there are four people randomly selected.

what is the probability that at least one of the four does not have access to recycling?

and then if none of the four had acces to recycling, is there evidence to suggest the claim is not correct?

.........

i know there are eighty six percent of everyone who recycle, i'm getting confused as to what information is relevant to find each question.
The probability that one person selected at random has access to recycling is $\displaystyle 0.86$. So the probability that all four do is $\displaystyle (0.86)^4=0.5470$ (4 d.p.)

Either (a) all have access; or (b) at least one does not. So the probability that at least one does not $\displaystyle = 1 - 0.5470 = 0.4530$ (4 d.p.)

The probability that a given person does not have access is $\displaystyle 1-0.86=0.14$. So the probability that all four do not have access is $\displaystyle (0.14)^4 = 0.0004$ (4 d.p.). So if none of the four people chosen had access, this suggests that the claim is incorrect.