Discussion
In a set of 30 game cards, 17 are white and rest are green. 4 white and 5 green are marked IMPORTANT. If a card is chosen randomly from this set, what is the possibility of choosing a green card or an ‘IMPORTANT’ card?
Answer: C
Of the 30 cards, 17 are white and 13 green. Nine are marked IMPORTANT: 4 white and 5 green.
Adding the two counts directly would double-count the 5 green IMPORTANT cards, so use the addition rule:
\[ P(G \cup I) = P(G) + P(I) - P(G \cap I) \]
\[ = \frac{13}{30} + \frac{9}{30} - \frac{5}{30} = \frac{17}{30} \]
Equivalently, count the 13 green cards plus the 4 white IMPORTANT ones: \( \tfrac{17}{30} \).
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