ITPEC FE Morning October 2019 Question 3
A candy box contains four flavors of candies: 6 lemon-flavored, 12 strawberry-flavored, 8 orange-flavored, and 4 grape-flavored. When a candy is randomly chosen from the box, what is the probability that it is either lemon- or orange-flavored?
Explanation
7/15 — one candy cannot be both lemon and orange, so add the two counts and divide by the total.
- •Total: 6 + 12 + 8 + 4 = 30 candies
- •Lemon or orange: 6 + 8 = 14 candies
- •Probability: 1430 = 715
Answer (b)
Why not others:
- •(d) 7/8 — 14 ÷ 16: the favourable candies divided by the other candies (12 + 4) instead of by all 30, which gives odds, not a probability
- •(a) 4/9 and (c) 6/11 — any probability of drawing from this box is a whole number of candies out of 30, and neither fits: 4/9 of 30 is 13.3 candies and 6/11 of 30 is 16.4
Key rule: For outcomes that cannot happen together, P(A or B) = P(A) + P(B), and the denominator is the whole sample, not the unfavourable outcomes.
Basic Theory · AI-written, may contain errors
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