E1 and E2 are mutually exclusive, then \(E_1∩ E_2=\)
- 1
- 5
- \(\phi\)
- None of these
The Correct Option is C
Solution and Explanation
Correct answer: \(\phi\)
Explanation:
Two events \( E_1 \) and \( E_2 \) are said to be mutually exclusive if they cannot occur at the same time. This means that the intersection of \( E_1 \) and \( E_2 \), denoted by \( E_1 \cap E_2 \), is the empty set, i.e., \( E_1 \cap E_2 = \emptyset \). Therefore, the value of \( E_1 \cap E_2 \) is \( \phi \), which represents the empty set.
Hence, \( E_1 \cap E_2 = \phi \).
Top Questions on Probability
Based upon the results of regular medical check-ups in a hospital, it was found that out of 1000 people, 700 were very healthy, 200 maintained average health and 100 had a poor health record.
Let \( A_1 \): People with good health,
\( A_2 \): People with average health,
and \( A_3 \): People with poor health.
During a pandemic, the data expressed that the chances of people contracting the disease from category \( A_1, A_2 \) and \( A_3 \) are 25%, 35% and 50%, respectively.
Based upon the above information, answer the following questions:
(i) A person was tested randomly. What is the probability that he/she has contracted the disease?}
(ii) Given that the person has not contracted the disease, what is the probability that the person is from category \( A_2 \)?- If A and B are two events such that $P(B) = \frac{1}{5}$, $P(A | B) = \frac{2}{3}$ and $P(A \cup B) = \frac{3}{5}$, then $P(A)$ is :
- If \( P(A) = \frac{1}{5}, P(B) = \frac{3}{5} \) and \( P(A \cap B) = \frac{2}{5} \), then \( P(A' \cup B') \) is :
- Bag I contains 4 white and 5 black balls. Bag II contains 6 white and 7 black balls. A ball drawn randomly from Bag I is transferred to Bag II and then a ball is drawn randomly from Bag II. Find the probability that the ball drawn is white.
- A meeting will be held only if all three members A, B and C are present. The probability that member A does not turn up is 0.10, member B does not turn up is 0.20 and member C does not turn up is 0.05. The probability of the meeting being cancelled is:
Questions Asked in AP POLYCET exam
- Area of a sector of a circle with radius 4 cm and angle 30° is (use \( \pi = 3.14 \)):
- The solution of \( x - 2y = 0 \) and \( 3x + 4y - 20 = 0 \) is:
- AP POLYCET - 2025
- Linear Equations
- If assumed mean of a data is 47.5, \( \sum f_i d_i = 435 \) and \( \sum f_i = 30 \), then mean of that data is:
- AP POLYCET - 2025
- Arithmetic Mean
- The points \( (1,5), (2,3) \) and \( (-2, -11) \) form a:
- A prime number \( p \) divides \( a^2 \) where \( a \) is a positive integer, then
- AP POLYCET - 2025
- Prime and Composite Numbers