(Slot machines) At a casino there are two kinds of slot machines, which look quite inden-tical from the outside. In machines of type A, the winning probability is 5%. In machines oftype B, the winning probability is 7%. We also know that 70% of the machines are of type A,and 30% are of type B.(a) A gambler picks a slot machine at random, and plays once. What is the probability thathe wins?(b) If the gambler wins, what is the probability that the machine is of type B?

event A : type A machine event B : type B machine event c : gambler wins P(A) = 0.70 P(B)= 0.30…

Answered: (Slot machines) At a casino there are…

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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Evan is ordering dessert, and he wants the fudge pie. The waitress tells him that he can have up to four toppings: ice cream, chocolate sauce, whipped cream, and a cherry. Since he cannot decide how many of the toppings he wants, he tells the waitress to surprise him. If the waitress randomly chooses which toppings to add, what is the probability that Evan gets just chocolate sauce, and a cherry.
Suppose you are on a game show and there are three closed doors. Behind one door is a car, and behind the other two doors are goats. Choose one door at random. What is the probability that you chose the winning door (the car)?
Consider the following game: A player rolls two dice. If he rolls 7 or less then he loses the game. Otherwise, he selects at random as many cards from the full deck as the sum of the numbers that came up on the dice. The player wins if all four Aces are among the selected cards. (a) What is the winning probability for this game? (b) Someone tells that he played this game once and won. What is the probability that he rolled a sum of 10?
Betty is offered a bet where she can win $100 dollars with a 1/4 chance and she would lose X with a 3/4 chance. She feels indifferent between taking the bet or not, and considers herself risk neutral, so X must be about. $25 O $33 O $80 O $66
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?
During class we found the probability of having as a hand the ”Royal Flush”. However, other pairs also exist in poker: Two-pair: Two cards have one rank, two cards have another rank, and the remaining card has a third rank. e.g. 2♥, 2♠, 5♥, 5♣, ��♦ Three-of-a-kind: Three cards have one rank and the remaining two cards have two other ranks. e.g. 2♥, 2♠, 2♣, 5♣, ��♦ Calculate the probability of each type of hand. Which is more likely
b. In oil exploration, the probability of an oil strike in the North Sea is 1 in 500 drillings. What is the probabilities of having exactly 3 oil producing wells in 1000 explorations? at most 2 oil producing wells in 800 drillings? Question-5
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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