Probability
Binomial Distribution
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>\(\dfrac{127}{128}\)</p>
<p>\(\dfrac{63}{64}\)</p>
<p>\(\dfrac{255}{256}\)</p>
<p>\(\dfrac{1}{2}\)</p>
Step-by-Step Solution
Key Concept: Use complementary probability: the only ways to NOT get at least one head AND at least one tail are getting all heads or all tails. Subtract these complement cases from 1.
<p><strong>Step 1:</strong> Find the total number of outcomes when tossing a coin 8 times: 2^8 = 256</p><p><strong>Step 2:</strong> Identify the complement of 'at least one head AND at least one tail': This is 'all heads OR all tails'</p><p><strong>Step 3:</strong> Count complement outcomes: P(all heads) = 1 outcome, P(all tails) = 1 outcome. Total complement outcomes = 2</p><p><strong>Step 4:</strong> Apply complement rule: P(at least one head and at least one tail) = 1 - P(all heads or all tails) = 1 - 2/256 = 1 - 1/128 = 127/128</p><p>∴ Answer: A</p>
Correct Answer: A