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: Understanding the Question:
We are drawing one ticket at random from a set of 50 tickets numbered 1 to 50. We want to find the probability that the number on this ticket is a multiple of 7.

Step 2: Key Formula or Approach:
The probability of an event \(E\) is given by:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]

Step 3: Detailed Explanation:

• The total number of outcomes is 50, since tickets are numbered 1 to 50.

• Identify the multiples of 7 between 1 and 50:
These are: \(7, 14, 21, 28, 35, 42, 49\).

• Count the number of favorable outcomes:
There are 7 multiples of 7 in this range.

• Calculate the probability:
\[ P(E) = \frac{7}{50} \]


Step 4: Final Answer:
The probability of drawing a multiple of 7 is \(\frac{7}{50}\).