Problem 4Suppose that the probability that a child has brown eyes is 2.Now consider a family with 4 children. For each i = 1,...,4 define the event B; that the ith childhas brown eyes. Assume that B₁,...,B4 are independent.(1) Using the events B₁,...,B4, describe the event that at least 3 children have brown eyes.(2) Compute the conditional probability that at least 3 children have brown eyes, given that thefirst child has brown eyes.

Answered: Image /qna-images/answer/5c925653-618f-4d4d-837c-0cde6534b207.jpg

Answered: Problem 4 Suppose that the probability…

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 two dice, one blue and one red, are rolled and the outcomes of each are recorded. We define the following two events: A: sum of the roll is 9 B. the result of the blue die is a number greater than 3 Are the two events, A and B, independent events? A. Yes B. No
If two events, A and B, are not independent, then the joint probability of event A and event B equals a. the conditional probability of event A given event B times the marginal probability of the event B b. the conditional probability of event B given event A times the marginal probability of the event A c. both of the above d. none of the above
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For each of these problems, you need to a) translate each sentence into probability notation, then b) determine if the specified events are independent. You must show work for independence. 1. The probability that a person plays on a high school basketball team is .031. The probability that a person plays on a high school baseball team is .04. The probability that a person plays on a high school baseball team and a high school basketball team is .017. Determine if the events "plays on a high school basketball team" and "plays on a high school baseball team" are independent events. 2. The probability that a person likes the superhero Iron Man is .46. The probability that a person likes the superhero Captain America is .58. The probability that a person likes the superhero Captain America given that the person likes the superhero Iron Man is .46. Determine if the events "likes Iron Man" and "likes Captain America" are independent events. 3. The probability that a person likes the…
An experiment consists of rolling a fair die twice. Let A be the event that in the second roll the die lands 1, 2, or 5; B be the event that in the second roll the die lands 4, 5, or 6; and C be the event that the sum of the two outcomes from the two rolls is 9. Please choose the correct answer:
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7. A dentist office needs toothbrushes and toothpaste to give to patients after each teeth cleaning appointment. The probability of not having an adequate supply of tooth- brushes is 0.3 while the probability of not having an adequate supply of toothpaste is 0.6. A study determines that the probability of a shortage of both toothbrushes and toothpaste is 0.4. Co Tur (a) For each given probability, define the event using symbols and words. (b) What is the probability that the dentist office experiences shortages ir either toothbrushes or toothpaste? fre
a) Show that for any three events A, B, and C, the probability that at least one of them occurs is P(A) + P(B) + P(C) - P(An B)- P(ANC) - P(BNC) + P(An BnC). b) Given A and B are independent events, with P(A) = 0.50 and P(B) = 0.30. Find P(ANB) c) About 52% of the residents of Capricorn municipality are happy and 48% of the residents are not happy with the delivery service. A recent study showed that 75% of happy residents and 25% of the unhappy residents are in favour of keeping the mayor of the municipality. If resident is randomly selected from the municipality residents is found to favour the motion. What is the probability that this person is happy with the delivery service?
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Events A and B are mutually exclusive. Suppose event A Occurs with probability 0.58 and event B occurs with probability 0.32. Compute the following. (If necessary, consult a list of formulas.) (a) Compute the probability that B occurs but A does not occur. (b) Compute the probability that neither the event A nor the event B occurs.

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