Question

Question 1 - section 3.1 In a city, the its citizens are either of high income (H) or low income (L). They use either their own car (C) or public transport (P) as a mode of daily commute. Assume: P(H) = 0.6,P(L) = 0.4. P(C) = 0.65,P(P) = 0.35, P(LIP) = 0.7;P(HIP) = 0.3 (i)Are the events H and L mutually exclusive? Why? (i) Are the events H and L independent? Why? (ii) Are the events P and L independent? iv) Compute the following probability A person who is high income and he uses public transport f a person is found to have high income, he drives his own car

Answer 1

a) Yes H and L are mutually exclusive as a person can either be of High Income group or Low, not both at a time.

b) H and L are dependent events and not independent. This is because Probability of One event ocurring here for Eg P(H) affects Probability of other P(L). Two events are said to be independent of each other when the probability that one event occurs in no way affects the probability of the other event occurring. For eh Probability of Head Coming in tossing a coin does not affect probability of 6 coming after rolling a dice.

c) P and L are independent events as for the reason given above. Probability of P and L doesnt affects each other.

d)

$P\left(\frac{P}{H}\right)=\frac{P\left(\frac{H}{P}\right).P\left(P\right)}{P\left(H\right)}$ USING BAYES' THEOREM

=0.3*.35/.6

=.175 IS THE PROBABILITY OF HIGH INCOME PEOPLE USING PUBLIC TRANSPORT

E) $P\left(\frac{C}{H}\right)=1-P\left(\frac{P}{H}\right)$

=1-.175

=0.825