According to Bayes’ Theorem, the
In Exercises 33–38, use Bayes’ Theorem to find P(A|B).
34. P(A) =
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Elementary Statistics: Picturing the World (7th Edition)
- The probability that a regularly scheduled flight departs on time is P(D)= 0.83; the probability that it arrives on time is P(A)=0.92; and the probability that it departs and arrives on time is P(D ∩ A)=0.78. Find the probability that a plane Arrives on time, given that it departed on time. Departed on time, given that it has arrived on time.arrow_forwardProve that P (a SXarrow_forwardd. Find the probability that X takes an even value. e. Find P(3 less than or equal to X less than or equal to 10)?arrow_forwardLet X and Y be independent, taking on {1,2,3,4,5} with equal probabilities. E((X+Y)2)=?arrow_forwardLet P(U)=0.06P(U)=0.06 and P(V)=0.44P(V)=0.44. Events UU and VV are mutually exclusive. Recall: P(A or B) = P(A) + P(B) - P(A and B)Find P(U or V)P(U or V).Is it correct answer 0.5?arrow_forwardassume that Pr[A∪B]=0.6 and Pr[A]=0.2 (1) What is Pr[B] if A and B are independent events?arrow_forwardThe probability of success in a certain game is p. The results in successive trials are independent Determine the generating function of Z and use the result to compute E(Z) and Var(Z) Let Z be the number of turns required in order to obtain r successes.arrow_forwardA piece of equipment will function only when the three components A, B and C are working. The probability of A failing during one year is 0.15, that of B failing is 0.05, and that of C failing is 0.10. What is the probability that the equipment will fail before the end of the year?arrow_forwardTo illustrate the proof of Theorem 1, consider the ran-dom variable X, which takes on the values −2, −1, 0, 1, 2, and 3 with probabilities f(−2), f(−1), f(0), f(1), f(2),and f(3). If g(X) = X2, find(a) g1, g2, g3, and g4, the four possible values of g(x);(b) the probabilities P[g(X) = gi] for i = 1, 2, 3, 4;(c) E[g(X)] = 4i=1gi ·P[g(X) = gi], and show that it equals xg(x)·f(x)arrow_forwardSuppose that A and B are independent events such that P(A) = 0.3 and P(B) = 0.2. Find P(A&B).arrow_forwardWe are given that P(A | B) = 0.2 and P(A) = 0.9. Since P(A | B) ≠ P(A), the occurrence of event B changes the probability that event A will occur. This implies that A and B are events.So, to determine P(A and B), we can apply the general multiplication rule for events. Recall that P(B) = 0.5. P(A and B) = P(B) · P(A | B) = (0.5) ·arrow_forwardEstimate the probability that a missile fired at speed x = 350 knots will hit the target.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage