Question

A car insurance company has determined that 9% of all drivers were involved in a car accident last
year. Among the 14 drivers living on one particular street, 3 were involved in a car accident last
year. If 14 drivers are randomly selected, what is the probability of getting 3 or more who were
involved in a car accident last year?
0.906
0.094
0.126
0.393

Answer 1

i tried the binomial distribution but now im just confused on where to start

Answer 2

can you tell me what you have so far

Answer 3

Well i though i could use b(x; n, P) – nCx * Px * (1 – P)n – x but i didnt work for me XD

Answer 4

can you figure out the probability of getting 0 of 14 who had an accident using the binomial distribution?

Answer 5

chance of getting 0 accidents : use n=14
x=0
P= 9% = 0.09
(1-P) = 0.91

Answer 6

If you can, then you would find the chance of getting 0 , 1 or 2 accidents out of 14
add up those 3 numbers
then 1- sum
is the chance of getting 3 or more accidents.

Answer 7

do i take (14)(0.09)+0.91?

Answer 8

isn't the formula
\[n C x \cdot P^x \cdot (1-P)^{n-x} \]
n choose x or in this case 14 C 0 is 1
(by definition, or use a calculator)
P^0 is 1
so you are left with
\[ 1 \cdot 1 \cdot (1-0.09)^{14} \]

Answer 9

i got 0.26704. so do id do that three times and add them together
?

Answer 10

yes, that looks good.
now find the probability of getting 1 accident out of 14

you do
14C1 * 0.09^1 * (1-0.09)^13

then for 2 accidents
14C2 * 0.09^2 * (1-0.09)^12

now add up the 3 numbers
and finally to find the probability of (not 0,1 or 2) (i.e. for 3 or more)
do
1- sum

Answer 11

0.267+0.238+0.370 = 0.875

Answer 12

1-0.875=0.125?

Answer 13

your 2nd two numbers are off.

Let's do x=1
14C1 * 0.09^1 * (1-0.09)^13

what do you get for 14 choose 1 ?
and 0.09 to the 1st power is just 0.09
and what do you get for 0.91^13 ?

Answer 14

14 choose 1 is 14 . and 0.91^13 is 0.293

Answer 15

ok, so you do
14*0.09*0.29345 (I would keep a few more decimals, and round at the end)

Answer 16

i got 0.370 like the last time

Answer 17

oh, I didn't notice you did them in a different order.
yes, then your numbers are ok (but you should have kept more decimals)

Answer 18

and after you do
1-0.875=0.125

that is close to the actual choice.

if you kept more decimals (at least 4)
then the final answer , when rounded, would be 0.126

Answer 19

Ahhh thank you so much i see what i did XD