A shop selling electronic items sells smartphones of only three reputed companies A, B, and C because chances of their manufacturing a defective smartphone are only 5%, 4%, and 2% respectively. In his inventory, he has 25% smartphones from company A, 35% smartphones from company B, and 40% smartphones from company C.
A person buys a smartphone from this shop
(i) Find the probability that it was defective.
A shop selling electronic items sells smartphones of only three reputed companies A, B, and C because chances of their manufacturing a defective smartphone are only 5%, 4%, and 2% respectively. In his inventory, he has 25% smartphones from company A, 35% smartphones from company B, and 40% smartphones from company C.
A person buys a smartphone from this shop
(i) Find the probability that it was defective.
Solution and Explanation
- \( A \): The event that the smartphone is from company A.
- \( B \): The event that the smartphone is from company B.
- \( C \): The event that the smartphone is from company C.
We are given: - \( P(A) = 0.25 \), \( P(B) = 0.35 \), \( P(C) = 0.40 \)
- \( P(D|A) = 0.05 \), \( P(D|B) = 0.04 \), \( P(D|C) = 0.02 \)
We need to find \( P(D) \), the total probability that a smartphone is defective.
Using the law of total probability: \[ P(D) = P(A) \cdot P(D|A) + P(B) \cdot P(D|B) + P(C) \cdot P(D|C) \] Substitute the values: \[ P(D) = 0.25 \times 0.05 + 0.35 \times 0.04 + 0.40 \times 0.02 \] \[ P(D) = 0.0125 + 0.014 + 0.008 \] \[ P(D) = 0.0345 \] Thus, the probability that the smartphone is defective is \( P(D) = 0.0345 \) or 3.45%.
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A shop selling electronic items sells smartphones of only three reputed companies A, B, and C because chances of their manufacturing a defective smartphone are only 5%, 4%, and 2% respectively. In his inventory, he has 25% smartphones from company A, 35% smartphones from company B, and 40% smartphones from company C.
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As you can see, a careful re-examination of the data can sometimes lead to a reversal of earlier interpretations. In this respect, it is necessary to mention the recent archaeogenetic research carried out at the site of Rakhigarhi. The site, located in Hisar district of Haryana, is the biggest Harappan city, spread over an area of 550 Hectare. In order to study the genetic history of the Harappans, DNA was extracted from the skeletal remains excavated at Rakhigarhi. This research was carried out by The Deccan College Deemed University, Pune in collaboration with Centre for Cellular and Molecular Biology, Hyderabad and The Harvard Medical College. The analysis of the data indicates that the Harappans are the indigenous people of this region.
The genetic roots of the Harappans go back to 10,000 BCE. The DNA of the Harappans has continued till today and a majority of the South Asian population appears to be their descendants. Due to trade and cultural contacts of the Harappans with distant regions there is a mixture of genes in small quantity. The continuity without any break in genetic history as well as cultural history rules out large scale immigration of the so-called Aryans. This research also indicates that the people coming from bordering areas and distant regions were absorbed in the Indian society. At no stage, the genetic history of the Indians was either discontinued or broken. As the Harappans started moving towards Iran and Central Asia, their genes also gradually spread in these regions.
The same team of researchers reconstructed 3D features of the Harappan people. The reconstructed facial features of the Harappans, male and female, show remarkable similarity with the modern population of Haryana. Thus, this study has indicated unbroken continuity for 5000 years in this region.
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Al-Biruni described Sanskrit as follows:
If you want to conquer this difficulty (i.e. to learn Sanskrit), you will not find it easy, because the language is of an enormous range, both in words and inflections, something like the Arabic, calling one and the same thing by various names, both original and derivative, and using one and the same word for a variety of subjects, which, in order to be properly understood, must be distinguished from each other by various qualifying epithets.- CBSE CLASS XII - 2025
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Maulvi Ahmadullah Shah was one of the many maulvis who played an important part in the revolt of 1857. Educated in Hyderabad, he became a preacher when young. In 1856, he was seen moving from village to village preaching jehad (religious war) against the British and urging people to rebel. He moved in a palanquin, with drumbeaters in front and followers at the rear. He was therefore popularly called Danka Shah – the maulvi with the drum danka. British officials panicked as thousands began following the maulwi and many Muslims began seeing him as an inspired prophet. When he reached Lucknow in 1856, he was stopped by the police from preaching in the city. Subsequently, in 1857, he was jailed in Faizabad. When released, he was elected by the mutinous 22nd Native Infantry as their leader. He fought in the famous Battle of Chinhat in which the British forces under Henry Lawrence were defeated. He came to be known for his courage and power. Many people in fact believed that he was invincible, had magical powers, and could not be killed by the British. It was this belief that partly formed the basis of his authority.
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On the same outline map, two places have been marked as ‘A’ and ‘B’, as the centres of the Revolt of 1857. Identify them and write their correct names on the lines drawn near them.
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