Answer to Question #197145 in Statistics and Probability for Sam

Question

box has 5 tickets numbered 1, 2, 3, 4 and 5. One 

of these tickets is drawn at random. 3 

i) If A = (1, 2) and B = {1), then show that P(B I A) 

> P(B) ii) If C = (1, 2, 3) and D = (1, 2, 4), then show that 

P(D I C) < P(D)

Answer 1

Given numbers-- 1,2,3,4,5

(i) A=(1,2), B={1}

$P(A)=\dfrac{2}{5}=0.4, P(B)= \dfrac{1}{5}=0.2,P(A\cap B)=\dfrac{1}{5}=0.2$

$P(B|A)=\dfrac{P(A\cap B)}{P(A)}=\dfrac{0.2}{0.4}=0.5>P(B)$

Hence, $P(B|A)>P(B)$

(ii) $C=(1,2,3),D=(1,2,4)$

$P(D)=\dfrac{3}{5}=0.6,P(C)=\dfrac{3}{5}=0.6,P(C\cap D)=\dfrac{2}{5}=0.4$

$P(D|C)=\dfrac{P(D\cap C)}{P(C)}=\dfrac{0.4}{0.6}=0.66<P(D)$

Hence, $P(D|C)<P(D)$ .