Probability
Independent Events
Grade 12
Question:
<p>A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. One fruit is picked out from each basket. The probability that the fruits are both apples or both oranges, is</p>
<p>(a) \(\frac{24}{144}\)</p>
<p>(b) \(\frac{56}{144}\)</p>
<p>(c) \(\frac{68}{144}\)</p>
<p>(d) \(\frac{76}{144}\)</p>
Step-by-Step Solution
Key Concept: Use the multiplication rule for independent events and addition rule for mutually exclusive events.
<p>Basket 1: 5 apples, 7 oranges (total 12)</p><p>Basket 2: 4 apples, 8 oranges (total 12)</p><p>Probability of both apples: \(\frac{5}{12} \times \frac{4}{12} = \frac{20}{144}\)</p><p>Probability of both oranges: \(\frac{7}{12} \times \frac{8}{12} = \frac{56}{144}\)</p><p>Total probability = \(\frac{20}{144} + \frac{56}{144} = \frac{76}{144}\)</p>
Correct Answer: D