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| Applications |
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| After the elementary study in probability, let us see how we can utilise this basic knowledge in solving problems of different areas. |
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| Example 1: |
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| In a housing colony 70% of the houses are well planned and 60% of the houses are well planned and well built. Find the probability that an arbitrarily chosen house in this colony is well built given that it is well planned. |
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| Suggested answer: |
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| Let A be the event that the house is well planned. B be the event that the house is well built. |
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| P (A) = 0.7 |
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| Probability that a house, selected is well built given that it is well planned. |
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| Example 2: |
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In a binary communication channel, A is the input and B is the  |
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| We know that |
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| We know that |
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| By Law of total probability |
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| Example 3: |
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| A manufacture ships his products in boxes of 10. He guarantees that not more than 2 out of 10 items are defective. If the probability that an item selected at random from his production line will be defective is 0.1, what is the probability that the guarantee is satisfied. |
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| Suggested answer: |
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| Let X be the random variable which represents number of defective items selected which has a binomial distribution with |
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| n = 10, p = 0.1, q = 0.9 |
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Probability that the guarantee is satisfied =  |
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