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The probability that it will rain on any particular day is 50%. Find the probability that it rains only on first 4 days of the week. |
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Answer» \((\frac{1}{2})^4(\frac{1}{2})^3=(\frac{1}{2})^7\) The experiment is rainfall in a week. The event that it will rain is success and the event that it will not rain is failure. Therefore, the probability of getting success is p = 50% = \(\frac{1}{2}\) The probability of getting failure is q = 1-p = \(\frac{1}{2}\) Rainfall in a week is binomial distribution whose parameters are n = 7 and p = \(\frac{1}{2}\) Now, the probability that it rains only on first 4 days of the week = 7C4 p4 q3 = \(\frac{7\times6\times5}{3!}\)\(\big(\frac{1}{2}\big)^4\big(\frac{1}{2}\big)^3\) = \(\frac{7\times6\times5}{3\times2}\big(\frac{1}{2}\big)^7\)= 35\(\big(\frac{1}{2}\big)^7\)= 35 x \(\frac{1}{128}\) = \(\frac{35}{128}\) |
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