SOLUTION: On a week night, the probability that Sonja watches TV is 0.4. If she watches TV, the probability that she does her homework is 0.3. The probability that she neither watches TV nor

Question 767053: On a week night, the probability that Sonja watches TV is 0.4. If she watches TV, the probability that she does her homework is 0.3. The probability that she neither watches TV nor does her homework is 0.2. What is the probability that on a week night Sonja does her homework?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
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 of the week nights that Sonja watches TV, of those nights she does homework.
That means that
of the nights Sonja watches TV and does homework,
while the remaining fraction of the week nights she just watches TV, but does not do her homework.

Since Sonja watches TV of the week nights, that means that
of the week nights she does not watch TV.
Within that of the week nights, there is the of the week nights when she neither watches TV nor does her homework.
The remaining of the week nights, Sonja does not watch TV, but she does her homework.

Adding up, Sonja does homework (52%) of the week nights.
The probability that on a week night Sonja does her homework is , (52%).
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