Maths Question

1) Given that a voter supports the liberal candidate, whatis the probability that he/she lives in state B?

Probability that a voter supports the liberal candidate:
50%*40%+60%*25%+35%*35%
=0.2+0.15+0.1225
=0.4725
P(the voter lives in State B & supports liberal candidate ∣the voter supports the liberal candidte)
= 60%*25% /0.4725
=0.15/0.4725
=0.317 (corr. to 3 sig. fig.) //

b) If it rains, an umbrella salesman canearn $300 per day. If it is cloudy, he can earn $25 perday. If it is fair, he can lose $60 per day. What is the salesman’s expectation if the probability of rain is 0.3and fair is 0.5 ?
Salesman'ts expectation =$300*0.3+ $25*0.2 - $60*0.5
=$90+$5 -$30
=$65 //

c) Bychecking several cartons containing large numbers of eggs, it was found thatthe average number of broken eggs a carton was 2.
Find: (i) theprobabilities of finding a carton containing 0, 1 and 2 brokeneggs; and
Using the poisson distribution
P(a carton containing 0)= e^(-2) (2)^0/0! =0.1353//
P(a carton containing 1)=e^(-2) (2)^1/1!=0.2707//
P(a carton containing 2)=e^(-2) (2)^2/2!=0.2707//

(ii) the probability of finding a cartoncontaining 3 or more broken eggs.
P(a carton containing 3 or more broken eggs)
=1-0.1353-0.2707-0.2707
=0.3233//