India play two matches each with West Indies and Australia. In any match the probabilities of India getting $$0,\,1$$ and $$2$$ points are $$0.45,\,0.05$$ and $$0.50$$ respectively. Assuming that the outcomes are independent, the probability of India getting at least $$7$$ points is :
A.
$$0.0875$$
B.
$$\frac{1}{{16}}$$
C.
$$0.1125$$
D.
none of these
Answer :
$$0.0875$$
Solution :
$$P\left( {{E_0}} \right) = 0.45,\,\,\,P\left( {{E_1}} \right) = 0.05,\,\,\,P\left( {{E_2}} \right) = 0.50$$
For $$7$$ points there should be at least three instances of $$2$$ points and one of $$1$$ or $$2$$ points.
$$\therefore $$ the required probability
$$\eqalign{
& = P\left( {{E_2}{E_2}{E_2}{E_2}} \right) + P\left( {{E_2}{E_2}{E_2}{E_1}} \right) + P\left( {{E_2}{E_2}{E_1}{E_2}} \right) + P\left( {{E_2}{E_1}{E_2}{E_2}} \right) + P\left( {{E_1}{E_2}{E_2}{E_2}} \right) \cr
& = {\left\{ {P\left( {{E_2}} \right)} \right\}^4} + 4{\left\{ {P\left( {{E_2}} \right)} \right\}^3}.P\left( {{E_1}} \right) \cr
& = {\left( {0.50} \right)^4} + 4{\left( {0.50} \right)^3}.\left( {0.05} \right) \cr
& = 0.0875 \cr} $$
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.
$$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$