Question

A box contains tickets numbered $1$ to $20$. $3$ tickets are drawn from the box with replacement. The probability that the largest number on the tickets is $7$, is

• A. $7/20$
• B. $1-(\frac{7}{30}{)}^3$
• C. $2/10$
• D. None of these

Answer 1

The correct option is D None of these

The tickets are numbered from $1$ to $20$ Let $A$ be the event that the chosen ticket ranges from $1$ to $6P\left(A\right)$$=\frac{6}{20}$

Now for the favourable event can occur in the following ways : $AA7,A7A,7AA$ Let's call this favourable event to be $E$$P\left(E\right)=P\left(A\right)\times P\left(A\right)\times P\left(7\right)+P\left(A\right)\times P\left(7\right)\times P\left(A\right)+P\left(7\right)\times P\left(A\right)\times P\left(A\right)=(\frac{6}{20}\times \frac{6}{20}\times \frac{1}{20})+(\frac{6}{20}\times \frac{1}{20}\times \frac{6}{20})+(\frac{1}{20}\times \frac{6}{20}\times \frac{6}{20})=\frac{27}{2000}$

Hence the correct option is $D$.

Final ans will be $127/8000$ pls check the solution.