<p>The probability of getting exactly 2 heads in tossing a coin thrice is \(\left(\frac{1}{8}\right)^n\).</p>
Step-by-Step Solution
Key Concept: Calculate the number of favorable outcomes (exactly 2 heads in 3 tosses) and divide by total outcomes (2³ = 8). The probability 3/8 must equal (1/8)ⁿ, so recognize that 3/8 ≠ (1/8)ⁿ for any integer n—the question likely contains a typo or asks to identify that the statement is false.
<p><strong>Step 1:</strong> Find total outcomes when tossing a coin thrice: 2³ = 8 outcomes</p><p><strong>Step 2:</strong> Find favorable outcomes (exactly 2 heads): HHT, HTH, THH = 3 outcomes</p><p><strong>Step 3:</strong> Calculate probability: P(exactly 2 heads) = 3/8</p><p><strong>Step 4:</strong> Check if 3/8 = (1/8)ⁿ. Since 3/8 ≠ 1/8, 1/64, 1/512, etc., the statement as written is <strong>FALSE</strong>. The correct statement should be P = 3/8 = 3·(1/2)³</p><p>∴ Answer: B (The statement is incorrect as formulated)</p>
Correct Answer: B