The prior probabilities for events A, and Az are P(A1) = 0.40 and P(A2) = 0.60. It is also known that P(A, n A2)=0. Suppose P(B|A1) = 0.10 and P(B|A2) = 0.20.a. Are events A1 and Ag mutually exclusive?Select your answer-Explain.(i) P(A1 N A2) = 0(ii) P(A1) + P(A2) = 1(iii) P(A2) P (A2 | A1)(iv) P(A2) = P(A2 | A1)- Select your ans wer - ♥b. Compute P(A1N B) (to 2 decimals).Compute P(A2 nB) (to 2 decimals).C. Compute P(B) (to 2 decimals).Apply Bayes' theorem to compute P(A1 B) (to 4 decimals).Also apply Bayes' theorem to compute P(A2|B) (to 4 decimals).

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Answered: The prior probabilities for events A1…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose A and B are events with P(A) = 0.3, P(B) = 0.65, and P(B|A) = 0.6.Find the value of P(A or B).
In a game of Chuck-a-Luck, a player can bet $1 on any one of the numbers 1, 2, 3, 4, 5, and 6. Three dice are rolled. If the player's number appears k times, where k > 1, the player gets $k back, plus the original stake of $1. Otherwise, the player loses the $1 stake. Some people find this game very appealing. They argue that they have a 1/6 chance of getting their number on each die, so at least a 1/6+1/6+1/6 = 50% chance of doubling their money. That's enough to break even, they figure, so the possible extra payoff in case their number comes up more than once puts the game in their favor. a) What do you think of this reasoning? b) Over the long run, how many cents per game should a player expect to win or lose playing Chuck-a-Luck?
The prior probabilities for events A1 and Ag are P(A1) = 0.50 and P(A2) = 0.50. It is also known that P(A n A2) = 0. Suppose P(B|A1) = 0.10 and P(B|A2) = 0.70. a. Are events Aj and Ag mutually exclusive? Yes Explain. (i) P(A1 N A2) = 0 (ii) P(A1) + P(A2) = 1 (iii) P(A2) + P (A2 | A1) (iv) P(A2) + P(A2 | A1) choice (i) b. Compute P(A1 n B) (to 2 decimals). 0.165 Compute P(A2 N B) (to 2 decimals). 0.4819 c. Compute P(B) (to 2 decimals). 0.415 d. Apply Bayes' theorem to compute P(A1|B) (to 4 decimals). Also apply Bayes' theorem to compute P(A2|B) (to 4 decimals).
A and B are two events. If P(A) =0.28, P(B) =0.30, P(A|B) =0.50 Find the P(A' and B)
Suppose we know that the probabilities P(A) = .5, P(B|A) = .3 and P(A or B) =.3. What is the value for P(A and B)? What is the value for P(B)?
A restaurant owner wanted to know which time range are popular among the customers. Data were collected on the following events: L = a customer usually visits the restaurant during lunch time D = a customer usually visits the restaurant during dinner time Data collected suggest the following: P( L ) = 0.6 P( D ) = 0.7 P( L and D) = 0.3 What is the possibility that a customer only visit the restaurant during dinner time
q15A -
Suppose that events E and F are independent with P(E) = 0.5 and P(F)=0.9 What is P(E and F)
Find the indicated probabilities: a. P(5sxs7); µ=6; o=2 ANS: b. P(10sxs16); µ=15; 0=4 ANS: c. P(7sxs9); H=5; o=2 ANS: d. P(1sxs2.6); µ=1.5; 0=0.4 ANS:
Suppose that events A and B are mutually exclusive with P(A) = 1 2 and P(B) = 1 6 . (Enter your answers as fractions.) (a) Are A and B independent events? Explain how you know. Since the events are mutually exclusive we know P(A|B) = which P(A) and thus the events are . (b) Are A and B complementary events? Explain how you know. We know that P(A) + P(B) = . And, since P(A) + P(B) 1, the events A and B complementary events.
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