1. ## probability help

A driver makes same trip everyday.he meets three trafic lights on trip. A study established that :
The probability of meeting three red lights is 0.2
The pobability of meeting atleast one red light is 0.8
The probability of meeting one red light is 0.3
Give the probability :
A:"meet exactly two red lights
B:"does not meet a red light"
C:"meet at most one red light"

I solved it as follows but am not sure :
A:0.3*0.3=0.09
B:1-0.2=0.8
C:1-0.8=0.2

2. ## Re: probability help

Hello, lebanon!

A driver makes same trip everyday.he meets three trafic lights on trip.
A study established that :
. . the probability of meeting three red lights is 0.2
. . the probability of meeting at least one red light is 0.8
. . the probability of meeting one red light is 0.3.

We are given:

. . $\displaystyle P(\text{3 red}) \:=\:0.2$

. . $\displaystyle P(\text{1, 2 or 3 red}) \:=\:0.8$

. . $\displaystyle P(\text{exactly 1 red}) \:=\:0.3$

Find the probability:

(a) meets exactly two red lights

$\displaystyle P(\text{exactly 2 reds}) \;=\;P(\text{1, 2, or 3 red}) - P(\text{1 red}) - P(\text{3 reds})$

. . . . . . . . . . . . . $\displaystyle =\;0.8 - 0.2 - 0.3 \;=\;0.3$

(b) does not meet a red light

The opposite of "no red lights" is "at least one red light".

$\displaystyle P(\text{no reds}) \;=\;1 - 0.8 \;=\;0.2$

(c) meets at most one red light.

"At most one red light" means: "no red lights" or "one red light".

$\displaystyle P(\text{at most one red}) \;=\;0.2 + 0.3 \:=\:0.5$