An author writes a good book with a probability of $1 / 2$ . If it is good is published with a probability of $2 / 3$ . If it is not, it is published with a probability of $1 / 4$ . Find the probability that he will get atleast one book published if he write two.

Open in App

Solution

Probability for one book to be published $= \frac{1}{2} (\frac{2}{3}) + \frac{1}{2} (\frac{1}{4}) = \frac{11}{24}$
$\frac{1}{2}$ it is good & published $\frac{1}{4}$ nor good & published
Probability no book is published $= 1 - \frac{11}{24} = \frac{13}{24}$
Probability that $2$ books are not published $= \frac{13}{24} (\frac{13}{24}) = \frac{169}{576}$
Probability that at least one book is published $= 1 - \frac{169}{576} = \frac{407}{576}$

Suggest Corrections

Similar questions

Q. The probability that a certain beginner at golf gets good shot if he uses correct club is

\frac{1}{3},

and the probability of a good shot with an incorrect club is

\frac{1}{4} .

In his bag there are 5 different clubs only one of which is correct for the good shot. If he chooses a club at random and take a stroke, the probability that he gets a good shot is

The probability that a person will get an electrification contract is $(\frac{2}{5})$ and the probability that he will not get a plumbing contract is $\frac{4}{7} .$ If the probability of getting at least one contract is $(\frac{2}{3})$ , what is the probability that he will get both ?