Probability
Classical Probability
Grade 12
Question:
<p>Before a race, the chances of runners \(A\), \(B\), \(C\) are proportional to 5:3:2. They are the only participants. Which are TRUE?</p>
Step-by-Step Solution
Key Concept: Probabilities proportional to 5:3:2 \to P(A)=5/10=1/2, P(B)=3/10, P(C)=2/10=1/5.
<p>Total ratio = 5+3+2=10.</p><p>$P(A)=\frac{5}{10}=\frac{1}{2}$ ✓ <strong>A</strong>.</p><p>$P(B)=\frac{3}{10}$ ✓ <strong>B</strong>.</p><p>$P(C)=\frac{2}{10}=\frac{1}{5}$ ✓ <strong>D</strong>.</p><p>$P(A\cup B)=\frac{1}{2}+\frac{3}{10}=\frac{8}{10}=\frac{4}{5}$ ✓ <strong>C</strong>.</p><p>All four are correct. ✓</p>
Correct Answer: ABCD