One hundred identical coins, each with probability of showing up a head, are tossed. If and if the probability of heads on exactly coins is equal to that of heads on exactly coins then the value of , is:

Explanation: Step 1: Set up the equality According to the question, . Step 2: Simplify the powers of and Divide both sides by and : Step 3: Expand the combinations Step 4: Cancel terms and solve Step 5: Substitute Conclusion: The value of is . Correct Option: (d)

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NIMCET 2010 — Mathematics PYQ

NIMCET | Mathematics | 2010

One hundred identical coins, each with probability $p$ of showing up a head, are tossed. If $0 < p < 1$ and if the probability of heads on exactly $50$ coins is equal to that of heads on exactly $51$ coins then the value of $p$ , is:

Choose the correct answer: