InterviewSolution
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InterviewSolution
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An experiment succeeds twice as often as it fails.Find the probability that in the next six trials, there will be atleast 4successes. |
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Answer» Let p be its probability of success and q be the failure. Then p =2q. Also, p+q=1. It gives `p=2//3and q=1//3.` P {4 successes in 6 trials} `=""^(6)C_(4)p^(4)q^(2)` `=""^(6)C_(4)((2)/(3))^(4)((1)/(3))^(2)" "(1)` P {5 successes in 6 trials} `=""^(6)C_(5)((2)/(3))^(5)((1)/(3))" "(2)` P{6 successes in 6 trials} `=""^(6)C_(6)((2)/(3))^(6)((1)/(3))^(0)" "(3)` Therefore, the probability that there are at least 4 successes is P {either 4 or 5 or 6 successes} `=""^(6)C_(4)((2)/(3))^(4)((1)/(3))^(1)+""^(6)C_(5)((2)/(3))^(5)((1)/(3))+""^(6)C_(6)((2)/(3))^(6)=496/729` |
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