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In Exercises 1–8, use Bayes’ theorem or a tree diagram to calculate the indicated probability. Round all answers to four decimal places. [HinT: See Quick Example 1 and Example 3.]
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Finite Mathematics and Applied Calculus (MindTap Course List)
- Many professional baseball teams (including the Cincinnati Reds and the Boston Red Sox) use Bill James's formula to estimate their probability of winning a league pennant: (Runs scored)2 (Runs scored)2 + (Runs allowed)2 Probability) of winning This formula, whose form is reminiscent of the Pythagorean theorem, is considered more accurate than just the proportion of games won because it takes into consideration the scores of the games.t Find this probability for a team that has scored 500 runs and allowed 400 runs. (Round your answer to the nearest whole percent.)arrow_forwardSection 2 7. The joint probability function for X and Y is given below. Find Pr(X >Y). fx,x (x, y) 0.24 0.36 1 0.21 0.19 0.79 0.43 None of the given options. 0.21 0.57arrow_forwardPart 2 of 2 What is the probability that a randomly chosen senior will have a GPA greater than 4.1? The probability that a randomly chosen senior will have a GPA greater than 4.1 is X Sarrow_forward
- Events A and B are independent with P(AB) = 0.2 and P(A'B) = 0.6. 3a. Find P(B).arrow_forwardYou are playing a game at a carnival. You can win $5 with probability 0.15 on each round, but if you lose, you pay $2. Assume each round that you play is independent of the others. Let X be the number of rounds it takes for you to get your first win (including the first win). X is distributed [ Select ] The expectation of X is [Select ] If you stop playing after your first win, your expected winnings (i.e. net profit, or the number of dollars you win or lose from playing the game; positive if you win more money than you lose) is [ Select ] You are playing a game at a carnival. You can win $5 with probability 0.15 on each round, but if you lose, you pay $2. Assume each round that you play is independent of the others. Let X be the number of rounds it takes for you to get your first win (including the first win). X is distributed [ Select ] [ Select ] The expectation of X Geometric(p = 0.15) Exponential(\lambda = 0.15) If you stop playing aft number of dollars you winnings (i.e. net…arrow_forwardCalculate the relative frequency P(E) using the given information. Six hundred adults are polled, and 480 of them support universal health-care coverage. E is the event that an adult supports universal health-care coverage. HINT [See Example 1.] P(E) = =arrow_forward
- %A. l. https://docs.google.com/fo YO 4.4 O 3.96 O 1.8 نقطة واحدة Let X denote the number of colleges where you will apply after your results and P(X =x) denotes your probability of getting admission in x number of colleges. It is given that if x = 0 or 1 if x = 2 if x 3 or 4 otherwise kx, 2kx, P(X = x) 3= %3D k(5 - x), 0, Where k is a positive constant. Then the probability that you will get admission in at most 2 colleges is 0.625arrow_forwardWhat do the functions Y. YY look like? Are there any maximum or 1+1 minimum probability at any particular angle(s) for these functions? [You don't have to prove this mathematically if you can provide your reasoning clearly.]arrow_forwardTask 2. Provide a proof of Theorem 3.3 part a. 106 Probability and Statistics with R Theorem 3.3 If a and b are real-valued constants, then (1) Mx+a(t) = E [e*+a)*] = eat . Mx(t).arrow_forward
- Section 1 4. The continuous random variable X has the following probability density function S{(1+æ), 0< x < 2; 0, fx (x) otherwise. The median, m, of a continuous random variable Y satisfies Pr(Y < m) = 0.5. Find the median of X. (Choose the option closest to the answer.) 0.8 1.4 1.2 1.6 1.0 Save For Later Nextarrow_forwardcalculate the relative frequency P(E) using the given information. Five hundred adults are polled, and 350 of them support universal health-care coverage. E is the event that an adult supports universal health-care coverage. HINT [See Example 1.] P(E) =arrow_forwardCalculate the relative frequency P(E) using the given information. Seven hundred adults are polled, and 490 of them support universal health-care coverage. E is the event that an adult supports universal health-care coverage. HINT [See Example 1.] P(E) =arrow_forward
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