Probability that a man who is $$40$$ year old, living till $$75$$ years is $$\frac{5}{{16}},$$ and another man who is $$35$$ years old living till $$70$$ years is $$\frac{3}{7}$$ then what is the probability that at least one of them will be alive till $$35$$ years hence ?
A.
$$\frac{{11}}{{28}}$$
B.
$$\frac{{19}}{{28}}$$
C.
$$\frac{{17}}{{28}}$$
D.
none of these
Answer :
$$\frac{{17}}{{28}}$$
Solution :
Let $$A$$ be the event that $${1^{st}}$$ man will be alive till $$75$$ years and $$B$$ be the event that $${2^{nd}}$$ man will be alive till $$70$$ years then $$P\left( A \right) = \frac{5}{{16}}$$ and $$P\left( B \right) = \frac{3}{7}$$ then $$P\left( {A'} \right) = \frac{{11}}{{16}}$$ and $$P\left( {B'} \right) = \frac{4}{7}.$$
Probability that none of them will be alive $$35$$ years hence is $$P\left( {A'} \right) \times P\left( {B'} \right) = \frac{{11}}{{16}} \times \frac{4}{7} = \frac{{11}}{{28}}$$
Then required probability is $$1 - \frac{{11}}{{28}} = \frac{{17}}{{28}}$$
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.
$$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$