Question

Each of the students in a particular class writes down a letter of her choice on a piece of paper and folds the paper to put it into a bowl. All the chosen letters are shown below.


Alex chooses a letter from the bowl randomly. What is the probability that Alex picks a paper with the first letter of his name written on it? After replacing the chosen paper with $‘\text{A'}$ in the bowl, he picks a letter again. What is the probability of picking the letter $‘\text{S'}$?

• A. $\frac{1}{17}$ and $\frac{4}{17}$
• B. $\frac{2}{17}$ and $\frac{3}{17}$
• C. $\frac{3}{17}$ and $\frac{2}{17}$
• D. None of the above

Answer 1

The correct option is A $\frac{1}{17}$ and $\frac{4}{17}$

$\bullet$ Total number of papers with letters in the bowl= $17$
Number of papers with letter $\text{A}$= $1$

$\text{Need to find:}$ Probability of picking a paper with first letter of the name Alex, i.e., $\text{P (A)}$

$\therefore \text{P(A)}=\frac{\text{Number of papers with letter A in the bowl}}{\text{Total number of papers in the bowl}}$

$\Rightarrow \underset{–}{\text{P(A)}=\frac{1}{17}}$

$\bullet$ As Alex replaces the paper with letter $‘\text{A'}$ in the bowl, the total number of papers still remains the same, which is $17$.

Number of papers with letter $‘\text{S'}$= $4$

$\therefore \text{P(S)}=\frac{\text{Number of papers with letter S in the bowl}}{\text{Total number of papers in the bowl}}$

$\Rightarrow \underset{–}{\text{P(S)}=\frac{4}{17}}$