Probability
Independent Events
Grade 12
Question:
<p>A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing on the fifth toss is equal to</p>
<p>(a) \(\frac{1}{2}\)</p>
<p>(b) \(\frac{1}{32}\)</p>
<p>(c) \(\frac{31}{32}\)</p>
<p>(d) \(\frac{1}{2}\)</p>
Step-by-Step Solution
Key Concept: Each coin toss is independent; previous outcomes do not affect future probabilities
<p>The fifth toss is independent of the previous four tosses. Each toss of a fair coin has P(Head) = 1/2, regardless of prior outcomes. P(Head on 5th toss | Tail on first 4 tosses) = P(Head on 5th toss) = 1/2</p>
Correct Answer: A