Probability
Conditional Probability
Grade 12
Question:
<p>Two dice are thrown. The probability that the number appeared have a sum of 8. If it is known that the second die always exhibits 4, is</p>
<p>(a) $$\frac{5}{6}$$</p>
<p>(b) $$\frac{1}{6}$$</p>
<p>(c) $$\frac{2}{3}$$</p>
<p>(d) $$\frac{1}{3}$$</p>
Step-by-Step Solution
Key Concept: Use conditional probability: given that the second die shows 4, find the probability that the sum is 8.
<p>Given that the second die shows 4, the sum is 8 when the first die shows 4.</p><p>Since the second die always shows 4, the only outcome where sum = 8 is (4,4).</p><p>The probability is $$\frac{1}{6}$$ (only one favorable outcome out of 6 possible outcomes for the first die).</p>
Correct Answer: B