Probability
Basic Probability
Grade 12
Question:
<p>In a lottery there were 90 tickets numbered 1 to 90. Five tickets were drawn at random. The probability that two of the tickets drawn numbers 15 and 89, is</p>
<p>(a) \(\frac{2}{801}\)</p>
<p>(b) \(\frac{2}{623}\)</p>
<p>(c) \(\frac{1}{267}\)</p>
<p>(d) \(\frac{1}{623}\)</p>
Step-by-Step Solution
Key Concept: Use combinations to count favorable outcomes where specific tickets are included among those drawn.
<p>Total ways to draw 5 tickets from 90: \(\binom{90}{5}\)</p><p>Favorable ways: Tickets 15 and 89 are drawn, plus 3 more from remaining 88: \(\binom{88}{3}\)</p><p>Probability = \(\frac{\binom{88}{3}}{\binom{90}{5}} = \frac{\binom{88}{3}}{\binom{90}{5}}\)</p><p>Computing: \(\frac{\binom{88}{3}}{\binom{90}{5}} = \frac{88 \times 87 \times 86}{90 \times 89 \times 88 \times 87 \times 86 / (5 \times 4 \times 3 \times 2 \times 1)} = \frac{10}{4005} = \frac{2}{801}\)</p>
Correct Answer: B