An experiment consists of two independent trials. The outcomes of the first trial are A, B, and C, with probabilities of occurring equal to 0.3, 0.3, and 0.4, respectively. The outcomes of the second trial are E and F, with probabilities of occurring equal to 0.5 and 0.5. Draw a tree diagram representing this experiment. Use this tree diagram to find the probabilities below. (a) P(B) (b) P(F | B) (c) P(B F) (d) P(F) (e) Does P(B F) = P(B) · P(F)? YesNo (f) Are B and F independent events

An experiment consists of two independent trials. The outcomes of the first trial are A, B, and C, with probabilities of occurring equal to 0.3, 0.3, and 0.4, respectively. The outcomes of the second trial are E and F, with probabilities of occurring equal to 0.5 and 0.5. Draw a tree diagram representing this experiment. Use this tree diagram to find the probabilities below. (a) P(B) (b) P(F | B) (c) P(B F) (d) P(F) (e) Does P(B F) = P(B) · P(F)? YesNo (f) Are B and F independent events

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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The accompanying tree diagram represents a two-stage experiment. (Let x = 0.3, y = 0.7, r = 0.7, s = 0.3, t = 0.4, and w = 0.6.) Use the diagram to find the following probabilities. (Round your answers to three decimal places.) (a) Find P(A) · P(D | A).(b) Find P(B) · P(D | B).(c) Find P(A | D).
blindness. Would these results be surprising? Explain why or why not. 4) At the end of basketball practice, each player on the team must shoot free throws until he makes 10 of them. Slim is a 70% free-throw shooter. That is, his probability of making any free throw is 0.70. Given this information, the dotplot below shows a simulation of 120 trials of shooting 12 free throws with a 0.70 chance of making any free throw. : 4 : 5 6 8 9 7 Number of Made Free Throws 10 11 red-green color 12 a) Explain what the two dots at 5 represents. b) Use the simulation to estimate the probability that Slim makes 10 or more free throws. 3 1297091 c) Based on the results from the simulation, how many free throws is Slim most likely to make in 12 attempts? d) Therefore, based on your answer to part (c), how many total attempted free throws do you predict Slim will have to take before he can finish practice and go home.
An experiment consists of two independent trials. The outcomes of the first trial are A, B, and C, with probabilities of occurring equal to 0.2, 0.4, and 0.4, respectively. The outcomes of the second trial are E and F, with probabilities of occurring equal to 0.7 and 0.3. Draw a tree diagram representing this experiment. Use this tree diagram to find the probabilities below. (a) P(B)(b) P(F | B)(c) P(B F)(d) P(F)(e) Does P(B F) = P(B) · P(F)? YesNo (f) Are B and F independent events? YesNo
The accompanying tree diagram represents an experiment consisting of two trials. Use the diagram to find the probabilities below. (a) P(A)(b) P(E | A)(c) P(A E)(d) P(E)
Let A and B be mutually exclusive events, such that P(A) = 0.2371 and P(B) = 0.1133. Find the following probabilities: P(A and B)= P(A or B)= % (Round the answer to 2 decimals) % (Round the answer to 2 decimals)
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In the election a state representative received 52% of the votes cast. One year after the election, the representative organized a survey that asked a random sample of 300 people whether they would vote for him in the next election. If we assume that his popularity has not changed, what is the probability that more than half of the sample would vote for him?
Example 2.17 Of the voters in a city, 40% are Republicans and 60% are Democrats. Among the Republicans 70% are in favor of a bond issue, whereas 80% of the Democrats favor the issue. If a voter is selected at random in the city, what is the probability that he or she favor the bond issue?
Given two events A and B, if P(A) = 0.4 and P(B) = 0.6, calculate the conditional probability P(A|B) if they are disjoint.
In an inspection of automobiles in a certain Country, 60% of all automobiles had emissions that did not meet EPA regulations. For a random sample of 10 automobiles, compute the following probabilities: a. All 10 automobiles failed the inspection. b. Exactly 6 of the 10 failed the inspection. c. Six or more failed the inspection. d. All 10 passed the inspection.
A kid has three remote controlled toy race cars and he plays with them 25%, 35% and 40% of the time respectively. The remote controls of the cars can sometimes malfunction, namely 5%, 7% and 9% of the time. If during a race the remote malfunctioned, what is the probability that he was playing with his third car? OA. 0.3356 OB. 0.1712 OC.0.4932 O D. 0.0360
Two events A and B have the following probabilities: P (A) = 0.4, P (B)= 0.5, and P (A and B) = 0.3. Find P( B and AC). Select one: a. 0.25 О Б. 0.7 c. 0.35 d. 0.2