Question

A shopkeeper has five customers who take cycle on rent. He has three cycles and the probability that customer will hire a cycle is $\frac{3}{4}$. If he charges rs.2 for a cycle as a rent, the probability that he earns exactly Rs.6 per day is $\frac{45k}{512}$. Find the value of $k$.

Answer 1

A is the event that the cycle is hired, so $P\left(A\right)=\frac{3}{4},P\left(\overrightarrow{A}\right)=\frac{1}{4}$
To earn Rs.6 per day his all the three cycles must be hired.
His cycles can be hired by 5 customers.
Hence the required probability ${=}^5{C}_3\cdot {\left(\frac{3}{4}\right)}^3\cdot {\left(\frac{1}{4}\right)}^2=\frac{135}{512}$.