Multiple choice

There are 58 balls in a jar. Each ball is painted with at least one of two colors, red or green. It is observed that 2/7 of the balls that have red color also have green color, while 3/7 of the balls that have green color also have red color. What is the probability that a ball randomly picked from the jar will have both red and green colors?

  1. 6/14

  2. 2/7

  3. 6/35

  4. 6/29

  5. 6/42
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let R be the set of balls with red color and G be the set of balls with green color. Given |R intersect G| / |R| = 2/7 and |R intersect G| / |G| = 3/7. This implies |R| = 3.5 * |R intersect G| and |G| = 2.33 * |R intersect G|. Using the principle of inclusion-exclusion, the total number of balls is 58. Solving the system yields the probability.

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