A boy is throwing stones at a target. The probability of hitting the target at any trial is $$\frac{1}{2}$$. The probability of hitting the target $${5^{th}}$$ time at the $${10^{th}}$$ throw is :
A.
$$\frac{5}{{{2^{10}}}}$$
B.
$$\frac{{63}}{{{2^9}}}$$
C.
$$\frac{{{}^{10}{C_5}}}{{{2^{10}}}}$$
D.
none of these
Answer :
$$\frac{{63}}{{{2^9}}}$$
Solution :
The probability of hitting the target $${5^{th}}$$ time at the $${10^{th}}$$ throw $$= P$$ (the probability of hitting the target $$4$$ times in the first $$9$$ throws) $$ \times $$ (the probability of hitting the target at the $${10^{th}}$$ throw)
$$\eqalign{
& = \left[ {{}^9{C_4}{{\left( {\frac{1}{2}} \right)}^4}{{\left( {\frac{1}{2}} \right)}^5}} \right]\left( {\frac{1}{2}} \right) \cr
& = \frac{{9!}}{{4!\,5!}} \times {\left( {\frac{1}{2}} \right)^{10}} \cr
& = \frac{{63}}{{{2^9}}} \cr} $$
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.
$$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$