Answer to Question #206882 in Statistics and Probability for kifayat

Question

the probability that a vehicle entering the lurvay carverns has Canadian lincense plate is 0.12 the probability that is a camper is 0.28, and the probability that is a camper with Canadian lincense is 0.09. what is the probability that

i. a camper entering the lurvay carverns has Canadian lincense,

a vehicle with Canadian lincense plate s entering the lurvay carverns is a camper

a vehicle entering the lurvay carverns does not have Canadian plates or is not a camper

Answer 1

Let $L$ denotes the event "a vehicle entering the lurvay carverns has Canadian lincense plate".

Let $C$ denotes the event "a vehicle entering the lurvay carverns is a camper".

Given $P(L)=0.12, P(C)=0.28, P(C\cap L)=0.09.$

i.

$$P(L|C)=\dfrac{P(C\cap L)}{P(C)}=\dfrac{0.09}{0.28}=\dfrac{9}{28}\approx 0.3214$$

ii.

$$P(C|L)=\dfrac{P(C\cap L)}{P(L)}=\dfrac{0.09}{0.12}=\dfrac{3}{4}=0.75$$

iii.

$$P(L'\cup C')=1-P(L\cap C)=1-0.09=0.91$$