From a pack of 52 cards, one card is drawn at random. Find the probability…

2024

From a pack of 52 cards, one card is drawn at random. Find the probability that the drawn card is a club or a jack?

  1. A.

    17/52

  2. B.

    8/13

  3. C.

    4/13

  4. D.

    1/13

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Show answer & explanation

Correct answer: C

This question falls under the category of Probability (which is associated with the Arithmetic topic from your provided syllabus).

Step-by-Step Solution

  1. Identify Total Possible Outcomes: A standard deck has 52 cards, so the total number of outcomes is 52.

  2. Count Favorable Outcomes: We want to draw either a "club" or a "jack".

    • There are 13 clubs in a deck.

    • There are 4 jacks in a deck.

    • However, one of these jacks is the "jack of clubs," which has been counted in both groups. To avoid double-counting, we must subtract this overlap.

    • Favorable outcomes = (Number of clubs) + (Number of jacks) - (Jack of clubs)

    • Favorable outcomes = 13 + 4 - 1 = 16.

  3. Calculate Probability: The probability is the number of favorable outcomes divided by the total number of outcomes.

    • Probability = 16 / 52.

  4. Simplify the Fraction: Both 16 and 52 are divisible by 4.

    • 16 divided by 4 = 4.

    • 52 divided by 4 = 13.

    • Final Probability = 4 / 13.

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