Question

14. The probability my daughter will eat her dinner without complaining is 5/7. The probability she will eat
her dinner and do her homework all without complaining is 2/7. What is the probability she will do her
homework without complaining given that she ate her dinner without complaining?

Answer 1

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.

$\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

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,

$P(B|A)= \dfrac{P(A\cap B)}{P(A)}$

             $= \dfrac{\dfrac{2}{7}}{\dfrac57}\\\\\\= \dfrac25$

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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