| List-I (Sentences) | List-II (Adverbs) |
| (A) \( P(A \cap B) \) | (I) \(\frac{2}{5}\) |
| (B) \( P(A | B) \) | (II)\( \frac{4}{15}\) |
| (C) \( P(A' | B) \) | (III) \(\frac{3}{5}\) |
| (D) \( P(A' \cap B') \) | (IV) \(\frac{2}{9}\) |
If A is any event associated with sample space and if E1, E2, E3 are mutually exclusive and exhaustive events. Then which of the following are true?
(A) \(P(A) = P(E_1)P(E_1|A) + P(E_2)P(E_2|A) + P(E_3)P(E_3|A)\)
(B) \(P(A) = P(A|E_1)P(E_1) + P(A|E_2)P(E_2) + P(A|E_3)P(E_3)\)
(C) \(P(E_i|A) = \frac{P(A|E_i)P(E_i)}{\sum_{j=1}^{3} P(A|E_j)P(E_j)}, \; i=1,2,3\)
(D) \(P(A|E_i) = \frac{P(E_i|A)P(E_i)}{\sum_{j=1}^{3} P(E_i|A)P(E_j)}, \; i=1,2,3\)
Choose the correct answer from the options given below:
Let A and B be two events such that: \[ P(A) = 0.8, \quad P(B) = 0.5, \quad P(B|A) = 0.4 \]
Match List-I with List-II:
| List-I | List-II |
|---|---|
| (A) \(P(A \cap B)\) | (I) 0.2 |
| (B) \(P(A|B)\) | (II) 0.32 |
| (C) \(P(A \cup B)\) | (III) 0.64 |
| (D) \(P(A')\) | (IV) 0.98 |
Rearrange the following parts to form a meaningful and grammatically correct sentence:
P. a healthy diet and regular exercise
Q. are important habits
R. that help maintain good physical and mental health
S. especially in today's busy world