5. Determine the probabilities of the following outcomes and events:(a) Tossing two coins and getting either one or two heads.(b) Randomly selecting a three-child family with exactly two girls.6. Suppose we toss a pair of standard six-sided dice.(a) What is the probability that we get a 7 (i.e., the sum of two faces is 7that vield a sevenMacBook Air80F4F5F6F7F3*#$&4ERY

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Answered: 5. Determine the probabilities of the…

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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Two coins are flipped. You win $1 if either 2 heads or 2 tails turn up, and you lose $3 if a head and a tail turn up. What is the expected value of the game?
In three independent flips of a coin where there is a 63% chance of flipping a tail, let A denote {first flip is a tail}, B denote {second flip is a tail}, C denote {first two flips are tails}, and D denote {three tails on the first three flips}. Find the probabilities of A, B, C, and D, and determine which, if any, pairs of these events are independent. P(A)= (Round to two decimal places as needed.) P(B)= (Round to two decimal places as needed.) P(C)= (Round to four decimal places as needed.) P(D)= (Round to four decimal places as needed.) Which of these pairs of events are independent? A. Events A and B because P(A and B)=P(A)•P(B). B. Events A and C because P(A and C)=P(A)•P(C). C. None of the pairs of events are independent. D. Events C and D because P(C and D)=P(C)•P(D)
1. An experiment is rolling two dice. Show work and give R for “given” probabilities. (a) State the sample space. (b) What is the probability that the sum is 7 given that the first die is a 2? (c)Are the two events sum of 6 and first die is a 5 independent events? Why or why not? (d) Are the two events sum of 7 and first die is a 2 independent events? Why or why not?
6. In a game of chance, a contestant must choose a number from one of three categories. Correct number choices in Category A are worth $1500, but there is a penalty of $1000 for each incorrect choice. Correct number choices in Category B are worth $1000, with a $500 penalty for each incorrect choice. Correct number choices in Category C are worth $500, with no penalty for an incorrect choice. The probability of choosing correctly is 0.05 for Category A, 0.15 for Category B, and 0.25 for Category C. Which category has the highest expected value? Find the exnected yalue for each of the unequal spinners shown. Inpors chown
Kevin is hiring two interns, and all applicants are either enrolled at Reading College (R) or Beekman College (B). He randomly picks two interns from the entire set of applicants. The tree diagram below shows the probabilities of the different outcomes. Based on the diagram, what is the probability of hiring two interns from Reading College? Provide the final answer as a fraction.

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5. Determine the probabilities of the following outcomes and events: (a) Tossing two coins and getting either one or two heads. (b) Randomly selecting a three-child family with exactly two girls.