Introduction To Probability Solutions to the Odd Numbered Exercises (Charles M. Grinstead &amp; J. L

# Introduction To Probability Solutions to the Odd Numbered Exercises (Charles M. Grinstead & J. L

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ω 2 = { A, B } ω 5 = { B, B } ω 8 = { C, B } ω 3 = { A, C } ω 6 = { B, C } ω 9 = { C, C } where the first grade is John’s and the second is Mary’s. You are given that P ( ω 4 ) + P ( ω 5 ) + P ( ω 6 ) = . 3 , P ( ω 2 ) + P ( ω 5 ) + P ( ω 8 ) = . 4 , P ( ω 5 ) + P ( ω 6 ) + P ( ω 8 ) = . 1 . Adding the first two equations and subtracting the third, we obtain the desired probability as P ( ω 2 ) + P ( ω 4 ) + P ( ω 5 ) = . 6 . 17. The sample space for a sequence of m experiments is the set of m -tuples of S ’s and F ’s, where S represents a success and F a failure. The probability assigned to a sample point with k successes and m - k failures is 1 n · k n - 1 n · m - k . (a) Let k = 0 in the above expression. (b) If m = n log 2, then lim n →∞ 1 - 1 n · m = lim n →∞ 1 - 1 n · n log 2 = lim n →∞ ( 1 - 1 n · n log 2 = e - 1 · log 2 = 1 2 .
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