Respuesta :
Answer:
a) 0.9523
b) 0.42
Step-by-step explanation:
Given:
husbands are watching television at prime time, P(H) = 0.80
husbands not watching television at prime time, P(H')= 1 - 0.80 = 0.20
When the husband is watching television, wife is also watching,
P( W | H ) = 0.50
When the husband is not watching television, wife is watching
⇒ P( W | H') = 0.10
Now,
a) The probability that wife is watching TV
⇒ P(W) = P( W | H')P(H') + P( W | H )P(H)
= (0.10 × 0.20) + (0.50 × 0.80)
= 0.02 + 0.4
= 0.42
By the Baye's theorem,
P( wife is watching television, when the husband is also watching tv)
⇒ P( H | W ) =[tex]\frac{P(W|H)P(H)}{P(W)}[/tex]
= [tex]\frac{0.50\cdot 0.80}{0.42}[/tex]
= 0.9523
b) P( wife is watching TV in prime time)
P(W) = P( W | H')P(H') + P( W | H )P(H)
= ( 0.10 × 0.20 ) + ( 0.50 × 0.80 )
= 0.02 + 0.4
= 0.42
