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A speaks truth in 75% cases and B in 80% of cases. In what percentage of cases they contradict each other in narrating the same incident?

A speaks truth in 75% cases and B in 80% of cases. In what percentage of cases they contradict each other in narrating the same incident? Correct Answer 35%

Probability that A is telling the truth P(A)
= $$\frac{{75}}{{100}}$$ = $$\frac{{3}}{{4}}$$
Probability that B is telling the truth P(B)
= $$\frac{{80}}{{100}}$$ = $$\frac{{4}}{{5}}$$
Probability that A is lying P(A’)
= 1 - $$\frac{{75}}{{100}}$$ = $$\frac{{25}}{{100}}$$ = $$\frac{{1}}{{4}}$$
Probability that B is lying P(B’)
= 1 - $$\frac{{80}}{{100}}$$ = $$\frac{{20}}{{100}}$$ = $$\frac{{1}}{{5}}$$
Contradiction means either of
A telling truth and B lying
            Or
B telling truth and A lying
P(Contradiction)
= P(A) × P(B’) + P(A’) × P(B)
= $$\frac{{3}}{{4}}$$ × $$\frac{{1}}{{5}}$$ + $$\frac{{1}}{{4}}$$ × $$\frac{{4}}{{5}}$$
= $$\frac{{7}}{{20}}$$
$$\frac{{7}}{{20}}$$ is equal to 35 %.

Related Questions

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Read the passage carefully and select the best answer to each question out of the given four alternatives.
What is Gandhian philosophy? It is the religious and social ideas adopted and developed by Gandhi, first during his period in South Africa from 1893 to 1914, and later of course in India. These ideas have been further developed by later "Gandhians", most notably, in India by, Vinoba Bhave and Jayaprakash Narayan. Outside of India some of the work of, for example, Martin Luther King Jr. can also be viewed in this light. Understanding the universe to be an organic whole, the philosophy exists on several planes - the spiritual or religious, moral, political, economic, social, individual and collective. The spiritual or religious element, and God, is at its core. Human nature is regarded as fundamentally virtuous. All individuals are believed to be capable of high moral development, and of reform. The twin cardinal principles of Gandhi's thought are truth and nonviolence. It should be remembered that the English word "truth" is an imperfect translation of the Sanskrit, "satya", and "non-violence", an even more imperfect translation of "ahimsa". Derived from "sat" - "that which exists" - "satya" contains a dimension of meaning not usually associated by English speakers with the word "truth". There are other variations, too, which we need not go into here. For Gandhi, truth is the relative truth of truthfulness in word and deed, and the absolute truth - the Ultimate Reality. This ultimate truth is God (as God is also Truth) and morality - the moral laws and code - its basis. Ahimsa, far from meaning mere peacefulness or the absence of overt violence, is understood by Gandhi to denote active love - the pole opposite of violence, or "Himsa", in every sense. The ultimate station Gandhi assigns non violence stems from two main points. First, if according to the Divine Reality all life is one, then all violence committed towards another is violence towards oneself, towards the collective, whole self, and thus "self"-destructive and counter to the universal law of life, which is love. Second, Gandhi believed that ahimsa is the most powerful force in existence. Had himsa been superior to ahimsa, humankind would long ago have succeeded in destroying itself. The human race certainly could not have progressed as far as it has, even if universal justice remains far off the horizon. From both viewpoints, non violence or love is regarded as the highest law of humankind.
According to Gandhiji, truth complies to which of the following?
Atal speaks the truth in 70% of the cases and George speaks the truth in 60% cases. In what percentage of cases are they likely to contradict each other in stating the same fact?
A speaks truth in 75% of cases and B in 80% of cases. In what percent of cases are they likely to contradict each other in narrating the same event?
Read the passage carefully and select the best answer to each question out of the given four alternatives.
What is Gandhian philosophy? It is the religious and social ideas adopted and developed by Gandhi, first during his period in South Africa from 1893 to 1914, and later of course in India. These ideas have been further developed by later "Gandhians", most notably, in India by, Vinoba Bhave and Jayaprakash Narayan. Outside of India some of the work of, for example, Martin Luther King Jr. can also be viewed in this light. Understanding the universe to be an organic whole, the philosophy exists on several planes - the spiritual or religious, moral, political, economic, social, individual and collective. The spiritual or religious element, and God, is at its core. Human nature is regarded as fundamentally virtuous. All individuals are believed to be capable of high moral development, and of reform. The twin cardinal principles of Gandhi's thought are truth and nonviolence. It should be remembered that the English word "truth" is an imperfect translation of the Sanskrit, "satya", and "non-violence", an even more imperfect translation of "ahimsa". Derived from "sat" - "that which exists" - "satya" contains a dimension of meaning not usually associated by English speakers with the word "truth". There are other variations, too, which we need not go into here. For Gandhi, truth is the relative truth of truthfulness in word and deed, and the absolute truth - the Ultimate Reality. This ultimate truth is God (as God is also Truth) and morality - the moral laws and code - its basis. Ahimsa, far from meaning mere peacefulness or the absence of overt violence, is understood by Gandhi to denote active love - the pole opposite of violence, or "Himsa", in every sense. The ultimate station Gandhi assigns non violence stems from two main points. First, if according to the Divine Reality all life is one, then all violence committed towards another is violence towards oneself, towards the collective, whole self, and thus "self"-destructive and counter to the universal law of life, which is love. Second, Gandhi believed that ahimsa is the most powerful force in existence. Had himsa been superior to ahimsa, humankind would long ago have succeeded in destroying itself. The human race certainly could not have progressed as far as it has, even if universal justice remains far off the horizon. From both viewpoints, non violence or love is regarded as the highest law of humankind.
What are the twin cardinal principles of Gandhis thought?
Read the passage carefully and select the best answer to each question out of the given four alternatives.
What is Gandhian philosophy? It is the religious and social ideas adopted and developed by Gandhi, first during his period in South Africa from 1893 to 1914, and later of course in India. These ideas have been further developed by later "Gandhians", most notably, in India by, Vinoba Bhave and Jayaprakash Narayan. Outside of India some of the work of, for example, Martin Luther King Jr. can also be viewed in this light. Understanding the universe to be an organic whole, the philosophy exists on several planes - the spiritual or religious, moral, political, economic, social, individual and collective. The spiritual or religious element, and God, is at its core. Human nature is regarded as fundamentally virtuous. All individuals are believed to be capable of high moral development, and of reform. The twin cardinal principles of Gandhi's thought are truth and nonviolence. It should be remembered that the English word "truth" is an imperfect translation of the Sanskrit, "satya", and "non-violence", an even more imperfect translation of "ahimsa". Derived from "sat" - "that which exists" - "satya" contains a dimension of meaning not usually associated by English speakers with the word "truth". There are other variations, too, which we need not go into here. For Gandhi, truth is the relative truth of truthfulness in word and deed, and the absolute truth - the Ultimate Reality. This ultimate truth is God (as God is also Truth) and morality - the moral laws and code - its basis. Ahimsa, far from meaning mere peacefulness or the absence of overt violence, is understood by Gandhi to denote active love - the pole opposite of violence, or "Himsa", in every sense. The ultimate station Gandhi assigns non violence stems from two main points. First, if according to the Divine Reality all life is one, then all violence committed towards another is violence towards oneself, towards the collective, whole self, and thus "self"-destructive and counter to the universal law of life, which is love. Second, Gandhi believed that ahimsa is the most powerful force in existence. Had himsa been superior to ahimsa, humankind would long ago have succeeded in destroying itself. The human race certainly could not have progressed as far as it has, even if universal justice remains far off the horizon. From both viewpoints, non violence or love is regarded as the highest law of humankind.
According to Gandhiji, what is the most powerful force in existence?
Read the passage carefully and select the best answer to each question out of the given four alternatives.
What is Gandhian philosophy? It is the religious and social ideas adopted and developed by Gandhi, first during his period in South Africa from 1893 to 1914, and later of course in India. These ideas have been further developed by later "Gandhians", most notably, in India by, Vinoba Bhave and Jayaprakash Narayan. Outside of India some of the work of, for example, Martin Luther King Jr. can also be viewed in this light. Understanding the universe to be an organic whole, the philosophy exists on several planes - the spiritual or religious, moral, political, economic, social, individual and collective. The spiritual or religious element, and God, is at its core. Human nature is regarded as fundamentally virtuous. All individuals are believed to be capable of high moral development, and of reform. The twin cardinal principles of Gandhi's thought are truth and nonviolence. It should be remembered that the English word "truth" is an imperfect translation of the Sanskrit, "satya", and "non-violence", an even more imperfect translation of "ahimsa". Derived from "sat" - "that which exists" - "satya" contains a dimension of meaning not usually associated by English speakers with the word "truth". There are other variations, too, which we need not go into here. For Gandhi, truth is the relative truth of truthfulness in word and deed, and the absolute truth - the Ultimate Reality. This ultimate truth is God (as God is also Truth) and morality - the moral laws and code - its basis. Ahimsa, far from meaning mere peacefulness or the absence of overt violence, is understood by Gandhi to denote active love - the pole opposite of violence, or "Himsa", in every sense. The ultimate station Gandhi assigns non violence stems from two main points. First, if according to the Divine Reality all life is one, then all violence committed towards another is violence towards oneself, towards the collective, whole self, and thus "self"-destructive and counter to the universal law of life, which is love. Second, Gandhi believed that ahimsa is the most powerful force in existence. Had himsa been superior to ahimsa, humankind would long ago have succeeded in destroying itself. The human race certainly could not have progressed as far as it has, even if universal justice remains far off the horizon. From both viewpoints, non violence or love is regarded as the highest law of humankind.
According to the passage, which of the following statement is not true?
A speaks truth in 60% cases B speaks truth in 70% cases. The probability that they will way say the same thing while describing a single event, is-