Question

According to an article, 31% of all cars crossing a toll bridge have a commuter sticker. What is the probability that among 15 randomly selected cars waiting to cross the bridge, at least 2 have commuter stickers? The probability that at least 2 cars have commuter stickers is. (Round to four decimal places as needed.)

Answer 1

The probability that the selected cars will have a sticker is independent of each other, and hence, binomial theorem is applied.

The probability that at least 2 cars will have stickers = 1-{probability no car will have stickers + probability 1 car will have a sticker}

The binomial theorem formula,which gives us the possibility of any x number of cars(in this case) have a sticker, is given by , where n is the number of trials(cars in this case), x is the number of cars having no stickers, p is the probability that any car has a commuter sticker, and q is the probability that that any car does not have a commuter sticker.

n=15,p=31%=0.31,q=1-0.31=0.69.

Probability no car has a sticker :{x=0}

= =

Probability that 1 car has a sticker: {x=1}

=
15C (0.31)'(0.69) 15-1

0.02578340219

Probability that at least 2 cars have a sticker =  1-{probability no car will have stickers + probability 1 car will have a sticker}

=

$1-(0.02578340219+0.00382592419)=1-0.02960932638=0.9704$

There is a 97.04% probability that at least 2 cars will have a sticker