Question

Q2 [40 points) A survey is conducted to find out whether people in metropoli- tan areas obtain their news from television (Event T), a newspaper (Event N), or radio (Event R). The results show that 60% of people get news on television, 60% from newspapers, 50% from radio, 30% from television and newspapers, 25% from television and radio, 30% from newspapers and ratio, and 15% from television, newspapers and radio.

Answer 1

From given informationwe have

$P(T)=0.60,P(N)=0.60,P(R)=0.50$

P(TIN) = 0.30, P(TNR) = 0.25, P(NOR) = 0.30, P(TINR) = 0.15

a)

P(TIN) = P(T) – PTON) = 0.60 – 0.30 = 0.30

Answer: 30%

b)

By the addition rule of probability we have

P(TUR) = P(T) + P(R) – PTR) = 0.60 + 0.50 -0.25 = 0.85

By the complement rule, the required probabilit is

$P[(T\cup R)']=1-P(T\cup R)=1-0.85=0.15$

Answer: 15%

c)

By the addition rule of probability we have

$P(T\cup N\cup R)=P(T)+P(N)+P(R)-P(T\cap N)-P(T\cap R)-P(R\cap N)+P(T\cap N\cap R)=0.60+0.60+0.50-0.30-0.25-0.30+0.15=1$

By the complement rule, the required probabilit is

$P[(T\cup N\cup R)']=1-P(T\cup N\cup R)=0$

Answer: 0%

d)

$P(N|R)=\frac{P(N\cap R)}{P(R)}=\frac{0.30}{0.50}=0.60$

Answer: 60%