Doubtly
@Doubtly · Joined Feb 2021
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- If A and B are events such that P(A/B) = P(B/A), then (A) A ⊂ B (B) B = A (C) A ∩ B = ∅ (D) P(A) = P(B) (D) P(A) = P(B) is correct option : P(A/B) = P(B/A) ⇒ P(A∩B)/P(B) = P(A∩B)/P(A) ⇒ P(A) = P(B) 1
- If P(A) = \(\frac{6}{11}\), P(B) = \(\frac{5}{11}\) and P(A ∪B) = \(\frac{7}{11}\) P(A ∪ B) = P(A) + P(B) – P(A ∩ B) (i) P(A ∩ B) = P(A) + P(B) – P(A ∪ B) = 6/11 + 5/11 – 7/11 = 4/11 (ii) P(A/B)=P(A∩ B)/P(B))=4/11/5/11=4/5... 1
- Evaluate P(A ∪ B), if 2P(A) = P(B) = \(\frac{5}{13}\) and P(A/B) = \(\frac{2}{5}\) We have: 2P(A) = P(B) = 5/13 ⇒ P(A) = 5/26 , P(B) = 5/13 . So, P(A/B) = P(A∩B)/P(B) or 2/5 = P(A cap B)/5/13 ⇒ P(A ∩ B) = 2/5 × 5/13 = 2/13... 1
- If P(A) = 0.8, P(B) = 0.5 and P(B/A) = 0.4, find (i) P(A ∩ B) (ii) P(A/B) (iii) P(A ∪ B) (i) P(B/A) = P(A∩B)/P(B) ⇒ 0.4 = P(A∩B)/0.8 ∴ P(A ∩ B) = 0.4 × 0.8 = 0.32. (ii) P(A/B) = P(A∩B)/P(B) = 0.32/0.5 = 32/50 = 16/25 . (iii) P(A... 1
- Compute P(A/B), if P(B) = 0.5 and P(A ∩ B) = 0.32. P(A/B) = P(A∩B)/P(B) = 0.32/0.5 = 32/50 = 16/25 1
- Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P(E/F) and P(F/E). P(E/F) = E∩F/P(F) = 0.2/0.3 = 2/3 . P(F/E) = P(E∩F)/P(E) = 0.2/0.6 = 2/6 = 1/3 . 1
- tan-1\(\sqrt{3}\) – cot-1(-\(\sqrt{3}\)) is equal to (A) π (B) \(\frac { π }{ 2 }\) (C) 0 (D) 2\(\sqrt{3}\) (B) π / 2 tan⁻¹ √(3) = tan⁻¹(tan π / 3 ) = π / 3 and cot⁻¹ √(3) = cot⁻¹(-cot π / 6 ) = cot⁻¹cot ( π – π / 6 ) = cot⁻¹cot 5π / 6 = 5π / 6 . s... 1
- What is PEAR in PHP? PEAR is a framework and repository for reusable PHP components. PEAR stands for PHP Extension and Application Repository. It contains all ty... 1
- Describe three daily life instances where viscosity plays an important role. Lubricating oils are viscous liquids. Gradation of lubricating oils is done on the basis of viscosity. A good quality lubricating oil does n... 1
- A balloon containing 0.6 mol of helium gas has a volume of 1.5 L. i. The volume of the balloon increases. ii. The volume of the balloon decreases. 2
- In an experiment conducted to study the diffusion of gases using same experimental conditions, following data i. Volume of gas A diffused = 50 cm³ Time required for diffusion = 7 minutes = 7 × 60 seconds Rate\ of\ diffusion\ of\ a\ gas =Volume\ of \... 1
- What makes the oil rise through the wick in an oil lamp? In an oil lamp, oil rises through the wick due to the capillary action. Such a capillary rise of oil is due to surface tension of oil. The w... 1
- Where is Dalton’s law applicable? Air is gaseous mixture of different gases. Dalton’s law is useful for the study of various phenomena in air, for example, air pollution. 1
- Do all pure gases and mixtures of gases obey the gas laws? Yes, the gas laws are also applicable to the mixtures of gases. The measurable properties of mixture of the gases such as pressure, temperat... 1
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- Explain the CSS Box Model. The CSS Box Model is useful for creating the design and layout of web documents. It is basically a box that is made up of different properti... 1