Probability
Independent Events
Grade 12
Question:
<p>A and B toss a fair coin each simultaneously 50 times. The probability that both of them will not get tail at the same toss is</p>
<p>(1) \((3/4)^{50}\)</p>
<p>(2) \((2/7)^{50}\)</p>
<p>(3) \((1/8)^{50}\)</p>
<p>(4) \((7/8)^{50}\)</p>
Step-by-Step Solution
Key Concept: In each toss, both get tails simultaneously with probability 1/4. The probability they DON'T both get tails is 1 - 1/4 = 3/4 per toss. Over 50 independent tosses, multiply the probabilities.
<p><strong>Step 1:</strong> Find probability that in a single toss, both A and B get tails simultaneously.</p><p>P(both get tails in one toss) = P(A gets tails) × P(B gets tails) = 1/2 × 1/2 = 1/4</p><p><strong>Step 2:</strong> Find probability that in a single toss, they do NOT both get tails.</p><p>P(not both get tails in one toss) = 1 - 1/4 = 3/4</p><p><strong>Step 3:</strong> Since tosses are independent, probability that this happens in all 50 tosses.</p><p>P(not both get tails in any of 50 tosses) = (3/4)^50</p><p>∴ Answer: A (which is (3/4)^50)</p>
Correct Answer: A