Probability helps us to know the chances of an event occurring. The probability she will do her homework without complaining given that she ate her dinner without complaining is 2/5.
What is Probability?
Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Let eating dinner without complaining be A, and doing homework without complaining be B.
Given the probability my daughter will eat her dinner without complaining is 5/7. So, we can write,
P(A) = 5/7
Also, The probability she will eat her dinner and do her homework all without complaining is 2/7. So, we can write,
P(A∩B) = 2/7
Now, the probability she will do her homework without complaining given that she ate her dinner without complaining is,
[tex]P(B|A)= \dfrac{P(A\cap B)}{P(A)}[/tex]
[tex]= \dfrac{\dfrac{2}{7}}{\dfrac57}\\\\\\= \dfrac25[/tex]
Hence, the probability she will do her homework without complaining given that she ate her dinner without complaining is 2/5.
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