Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the…

2024

Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7?

  1. A.

    9/25

  2. B.

    9/50

  3. C.

    18/25

  4. D.

    18/20

Attempted by 10 students.

Show answer & explanation

Correct answer: A

Step-by-Step Solution

  1. Identify Total Outcomes: There are 50 tickets numbered from 1 to 50, so the total number of outcomes is 50.

  2. Count Multiples of 4: To find the multiples of 4 up to 50, divide 50 by 4. The result is 12 (since 4 × 12 = 48).

  3. Count Multiples of 7: To find the multiples of 7 up to 50, divide 50 by 7. The result is 7 (since 7 × 7 = 49).

  4. Identify Overlaps (Multiples of both 4 and 7): These are multiples of 28 (the least common multiple of 4 and 7). Up to 50, only 28 fits this category (count = 1).

  5. Calculate Favorable Outcomes: Using the addition rule, add the count of multiples of 4 and multiples of 7, then subtract the overlap to avoid double-counting.

    • Favorable outcomes = 12 + 7 - 1 = 18.

  6. Calculate Probability: Probability is favorable outcomes divided by total outcomes.

    • Probability = 18 / 50.

    • Simplifying the fraction (dividing both by 2) results in 9 / 25.

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