In a set of 30 game cards, 17 are white and the rest are green. Out of the 30, 4 white and 5 green are marked “IMPORTANT”. If a card is chosen randomly from this set, the possibility of choosing a green card or an “IMPORTANT” card is:
Show Hint
Use: \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \)
Don’t forget to subtract the intersection
Always check overlap between categories
- \( \frac{13}{30} \)
- \( \frac{22}{30} \)
- \( \frac{17}{30} \)
- \( \frac{9}{13} \)
The Correct Option is C
Solution and Explanation
White = 17, Green = \(30 - 17 = 13\)
“IMPORTANT” cards = 4 white + 5 green = 9 Let \(A\): event that the card is green = 13 cards
Let \(B\): event that card is “IMPORTANT” = 9 cards
Overlap = 5 (green & important) \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) = \frac{13}{30} + \frac{9}{30} - \frac{5}{30} = \frac{17}{30} \]
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