Probability
Classical Probability
Grade 12
Question:
<p>An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is:</p>
<p>\(\dfrac{63}{64}\)</p>
<p>\(\dfrac{255}{256}\)</p>
<p>\(\dfrac{127}{128}\)</p>
<p>\(\dfrac{1}{2}\)</p>
Step-by-Step Solution
Key Concept: Use complementary probability: P(at least one H and at least one T) = 1 - P(all H or all T). The complement of 'at least one of each' is getting only heads or only tails.
<p><strong>Step 1:</strong> Total possible outcomes when tossing a coin 8 times = 2^8 = 256</p><p><strong>Step 2:</strong> Identify the complement of 'at least one H and at least one T':</p><p>Complement = (all heads) OR (all tails)</p><p>Number of outcomes with all heads = 1</p><p>Number of outcomes with all tails = 1</p><p>Total unfavorable outcomes = 1 + 1 = 2</p><p><strong>Step 3:</strong> Apply complementary probability:</p><p>P(at least one H and at least one T) = 1 - P(all H or all T)</p><p>= 1 - 2/256</p><p>= 1 - 1/128</p><p>= 127/128</p><p>∴ Answer: B</p>
Correct Answer: B