A fair coin is tossed $$99$$ times. If $$X$$ is the number of times head occurs, $$P\left( {X = r} \right)$$ is maximum when $$r$$ is :
A.
49 or 50
B.
50 or 51
C.
51
D.
none of these
Answer :
49 or 50
Solution :
$$\eqalign{
& {\text{Putting}}\,n = 99{\text{ and }}p = \frac{1}{2},{\text{we have}} \cr
& \left( {n + 1} \right)p = \left( {100} \right)\left( {\frac{1}{2}} \right) = 50 \cr
& {\text{so that the maximum value of }}P\left( {X = r} \right) \cr
& {\text{occurs at }}r = \left( {n + 1} \right) \cr
& p = 50{\text{ and }}r = \left( {n + 1} \right)p - 1 = 49 \cr} $$
Releted MCQ Question on Statistics and Probability >> Probability
Releted Question 1
Two fair dice are tossed. Let $$x$$ be the event that the first die shows an even number and $$y$$ be the event that the second die shows an odd number. The two events $$x$$ and $$y$$ are:
Two events $$A$$ and $$B$$ have probabilities 0.25 and 0.50 respectively. The probability that both $$A$$ and $$B$$ occur simultaneously is 0.14. Then the probability that neither $$A$$ nor $$B$$ occurs is
The probability that an event $$A$$ happens in one trial of an experiment is 0.4. Three independent trials of the experiment are performed. The probability that the event $$A$$ happens at least once is
If $$A$$ and $$B$$ are two events such that $$P(A) > 0,$$ and $$P\left( B \right) \ne 1,$$ then $$P\left( {\frac{{\overline A }}{{\overline B }}} \right)$$ is equal to
(Here $$\overline A$$ and $$\overline B$$ are complements of $$A$$ and $$B$$ respectively).
A.
$$1 - P\left( {\frac{A}{B}} \right)$$
B.
$$1 - P\left( {\frac{{\overline A }}{B}} \right)$$
C.
$$\frac{{1 - P\left( {A \cup B} \right)}}{{P\left( {\overline B } \right)}}$$
D.
$$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$