probability of booking


What is the probability of all events occurring?

    The probability of all of the events occurring is simply the product of allof the individual probabilities. (b) The reasoning in part (a) works again, with only slight modi?cations. If weperform a large number of trials, thenAoccurs in a fractionP(A)of them.And thenBoccurs in a fractionP(B|A)of thesetrials, by de?nition.

What is the probability of a matching pair?

    Andif we look ats5?rst and then ats6, we can use the reasoning in part (c) ofProblem 2.9 to say that the probability of a matching pair is(n?1)/(2n?1).This reasoning works for any of thenpairs; there is nothing special about aspeci?c pair (assuming we haven’t looked at any of the other pairs).

How do you calculate probabilities?

    Two common ways to calculate probabilities are: (1) count up the number ofdesired outcomes, along with the total number of possible outcomes, and useEq. (2.68) (assuming that the outcomes are equally likely), and (2) imaginethings happening in succession (for example, picking seats or rolling dice),and then multiply the relevant probabilities.

What is the probability of complete success all the way through?

    Theprobability of complete success all the way through is therefore in agreement with the ?rst solution. Note that if we write the initial 1 here as 6/6, thenthis expression becomes 6!/66, which is the fraction that appears in Eq. (2.35). Example 2 (Three pairs): Six dice are rolled.
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