Question

One ticket is drawn at random from a bag containing 50 tickets numbered 1 to 50. The probability that the drawn ticket has a number which is a multiple of 7 is :

• A. \(\frac{1}{5}\)
• B. \(\frac{7}{50}\)
• C. \(\frac{3}{25}\)
• D. \(\frac{4}{25}\)

Hint:

To quickly find how many multiples of a number \(k\) lie in the range from 1 to \(N\), perform integer division:
\[ \lfloor 50 / 7 \rfloor = 7 \]
This guarantees you won't miss any values!

Answer 1

The Correct Option is B

Step 1: Recognise the multiples of 7 as an AP.
The multiples of 7 up to 50 are $7, 14, 21, \dots$, forming an AP with first term 7 and common difference 7.
Step 2: Count the terms using the AP term formula.
We need the largest $n$ with $7n \le 50$, i.e. $n \le \frac{50}{7} \approx 7.14$, so $n = 7$.
Step 3: Compute the probability.
\[ P(\text{multiple of } 7) = \frac{7}{50} \]
\[ \boxed{\frac{7}{50}} \]