Question 767053
The probability that Sonja watches TV on a week night is 0.4.
If she watches TV, the probability that she does her homework is 0.3.
So, of the {{{0.4=4/10}}} of the week nights that Sonja watches TV, {{{0.3=3/10}}} of those nights she does homework.
That means that
{{{0.4*0.3=0.12}}} of the nights Sonja watches TV and does homework,
while the remaining {{{0.4-0.12=0.28}}} fraction of the week nights she just watches TV, but does not do her homework.
 
Since Sonja watches TV {{{0.4=4/10}}} of the week nights, that means that
{{{1-0.4=0.6}}} of the week nights she does not watch TV.
Within that {{{0.6}}} of the week nights, there is the {{{0.2}}} of the week nights when she neither watches TV nor does her homework.
The remaining {{{0.6-0.2=0.4}}} of the week nights, Sonja does not watch TV, but she does her homework.
 
{{{drawing(300,300,-10,110,-10,110,
rectangle(0,0,100,100),
line(0,60,100,60), line(70,60,70,100),
line(30,0,30,60),locate(80,100,0.3),
locate(1,85,0.4),
locate(55,35,no),locate(65,35,TV),locate(60,30,HW),locate(55,25,(0.40)),
locate(8,35,no),locate(16,35,TV),
locate(8,30,no),locate(16,30,HW),locate(7,25,(0.20)),
locate(32,90,TV),locate(27,85,no),locate(36,85,HW),locate(27,80,(0.28)),
locate(82,90,TV),locate(75,85,and),locate(87,85,HW),locate(77,80,(0.12))
)}}}
Adding up, Sonja does homework {{{0.12+0.4=0.52}}} (52%) of the week nights.
The probability that on a week night Sonja does her homework is {{{highlight(0.52)}}}, (52%).