A six faced fair dice is thrown until 1 comes, then the probability that 1 comes in even no. of trials is
A.
$$\frac{5}{{11}}$$
B.
$$\frac{5}{{6}}$$
C.
$$\frac{6}{{11}}$$
D.
$$\frac{1}{{6}}$$
Answer :
$$\frac{5}{{11}}$$
Solution :
In single throw of a dice, probability of getting 1 is = $$\frac{1}{6}$$
and prob. of not getting 1 is $$\frac{5}{6}$$
Then getting 1 in even no. of chances = getting 1 in $${2^{nd}}$$ chance or in $${4^{th}}$$ chance or in $${6^{th}}$$ chance and so on
∴ Req. Prob. $$ = \frac{5}{6} \times \frac{1}{6} + {\left( {\frac{5}{6}} \right)^3} \times \frac{1}{6} + {\left( {\frac{5}{6}} \right)^5} \times \frac{1}{6} + .....\,\infty $$
$$\eqalign{
& = \frac{5}{{36}}\left[ {\frac{1}{{1 - \frac{{25}}{{36}}}}} \right] \cr
& = \frac{5}{{36}} \times \frac{{36}}{{11}} \cr
& = \frac{5}{{11}} \cr} $$
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.
$$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$