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Most probable number of successes (mode) of a binomial

This type of question, asked 2 times: 20 Apr 2025 S2, 13 Apr 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    20 Apr 2025 S2

    150
    A fair coin is tossed 99 times. If X is the number of times head occur, then P[X=r]P\lbrack X = r\rbrack is maximum when r=r =

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  2. Question 2

    13 Apr 2026 S1

    100
    Let X∼B(6,12)X \sim B\left(6, \dfrac{1}{2}\right). Then the maximum probability occurs at

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