Doubtly
@Doubtly · Joined Feb 2021
- Answers
- 3,792
- Questions
- 4,033
- Upvotes received
- 424
- The probability of obtaining an even prime number on each die, when a pair of dice is rolled is There are only one even prime number, i.e., 2, when a dice is rolled, the probability of getting an even prime number = 1/6 . When two dice... 1
- Two events A and B are said to be independent, if (A) A and B are mutually exclusive. (B) P(A’B’) (B) P(A’B’) = [1 – P(A)] [1 – P(B)] Two events are independent, if P(A ∩ B) = P(A) × P(B) or P(A’ ∩ B’) = P(A’) P(B’) = [1 – P(A)][1 – P(B)] 1
- Given that two numbers appearing on throwing two dice are different. Find the probability of the event When the numbers appearing on throwing two dice are different. ⇒ The numbers are not the same Total number of exhaustive cases = 36 Number o... 1
- Consider the experiment of throwing a dice, ‘if a multiple of 3 comes up, throw the dice again and if any other number The outcomes of the given experiment can be represented by the following tree diagram. The sample space of the experiment is, S=(1,H),(1,T),... 1
- If P(A) = \(\frac{1}{2}\), P(B) = 0, then P(A/B) is (A) 0 (B) \(\frac{1}{2}\) (C) not defined (D) 1 (C) not defined P(A) = 1/2 , P(B) = 0 P(A/B) = P(A∩B)/P(B) = P(A∩B)/0 = Not defined. 1
- 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
- How to convert 20.1741 to 2.02 20.1741 = 20.17 =20.2 {rounding of to nearest number} then it can be = 20.2 and 2.02 x 10 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