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Axiomatic Approach

A fair coin i...

Question

A fair coin is tossed $99$ times. Let $X$ be the number of times heads occurs. Then $P (X = r)$ is maximum when $r$ is

A

49

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B

52

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C

51

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D

50

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Solution

The correct option is D $50$
The probability that head appears $r$ times is $^{99} C_{r} {(\frac{1}{2})}^{r} {(\frac{1}{2})}^{99 - r}$
which is maximum when $r = 49$ or $50$

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