Multiple choice

In n coins are thrown then number of elements in sample space of event appearing number of heads

  1. nC0 + nC1 + nC2 +…. nCn

  2. nC0 nC2 + nC4 +….

  3. nC1 + nC3 + nC5 +….

  4. 2n+1
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A Correct answer
Explanation

The sample space for n coins tossed is the set of all possible outcomes, which has 2^n elements. The sum of binomial coefficients nC0 + nC1 + ... + nCn equals 2^n, which represents the total number of subsets or outcomes.

AI explanation

When n coins are thrown, the total number of elements in the sample space is 2^n. This sample space can be partitioned into events based on the exact number of heads appearing, ranging from zero heads to n heads. The number of outcomes with k heads is given by the combination nCk, so the total number of elements is the sum of these combinations for all values of k from 0 to n. Therefore, the sample space size is represented by nC0 + nC1 + nC2 + ... + nCn.

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