A die is thrown. Let $$A$$ be the event that the number obtained is greater than 3. Let $$B$$ be the event that the number obtained is less than 5. Then $$P\left( {A \cup B} \right)$$ is
A.
$$\frac{3}{5}$$
B.
0
C.
1
D.
$$\frac{2}{5}$$
Answer :
1
Solution :
$$A$$ $$ \equiv $$ number is greater than 3
$$ \Rightarrow \,\,P\left( A \right) = \frac{3}{6} = \frac{1}{2}$$
$$B$$ $$ \equiv $$ number is less than 5
$$ \Rightarrow \,\,P\left( B \right) = \frac{4}{6} = \frac{2}{3}$$
$$A \cap B \equiv $$ number is greater than 3 but less than 5.
$$\eqalign{
& \Rightarrow \,\,P\left( {A \cap B} \right) = \frac{1}{6} \cr
& \therefore P\left( {A \cup B} \right) = P\left( A \right) + P\left( B \right) - P\left( {A \cap B} \right) \cr
& = \frac{1}{2} + \frac{2}{3} - \frac{1}{6} \cr
& = \frac{{3 + 4 - 1}}{6} \cr
& = 1 \cr} $$
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.
$$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$