Consider an experiment of tossing two fair coins. Let X be a random variable denoting the outcomes "head or tail" of the first coin and Y be another random variable denoting the outcomes of another coin. Find the joint probability matrix.
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- In women’s tennis, a player must win 2 out of 3 sets to win a match. If a player wins the first 2 sets, she wins the match and the third set is not played. Player V and Player M will compete in a match. Player V and Player M have competed against each other many times. Historical data show that each player is equally likely to win the first set. If Player V wins the first set, the probability that she will win the second set is 0.60. If Player V loses the first set, the probability that she will lose the second set is 0.70. If Player V wins exactly one of the first two sets, the probability that she will win the third set is 0.45. What is the probability that Player V will win a match against Player M?Two machines turn out all the paper bags produced in the plant. Machine A produces 38% of the bags and machine B produces 62% of the bags. Machine A produces defective bags 1.9% of the time and machine B produces defective bags 3.8% of the time. Given a defective bag, what is the probability that it came from machine B?If you have a sample of 100 patients at a hospital and 20 of them have the flu, what is the probability Of randomly selecting 3 patients in a row who have the flue?
- A shipment of 7 microwave ovens contains 2 defective units. A restaurant buys four of these units. What is the probability of the restaurant buying at least three nondefective units? The probability of the restaurant buying at least three nondefective units isIn 2013, the total sales from 3 different car production companies was 606,334 cars or light trucks. The probability that the vehicle was made by Company A was 0.386, by Company B 0.350, and by Company C 0.258. Additionally, the probability that a Company A vehicle sold was a car was 0.379, a Company B vehicle sold was a car was 0.370, and a Company C vehicle sold was a car was 0.332. Given the vehicle sold was a car, find the probability it was made by Company A. The probability a vehicle was made by Company A, given it was a car is (Round to three decimal places as needed.)A batch of parts contains 80 parts from batangas supplier of engine and 120 parts from a supplier of engine in bulacan. If five parts are selected randomly and without replacement, find the probability that: atleast one part in the supplier from Batangas.
- In 2013, the total sales from 3 different car production companies was 606,334 cars or light trucks. The probability that the vehicle was made by Company A was 0.381, by Company B 0.350, and by Company C 0.258. Additionally, the probability that a Company A vehicle sold was a car was 0.385, a Company B vehicle sold was a car was 0.370, and a Company C vehicle sold was a car was 0.332. Given the vehicle sold was a car, find the probability it was made by Company A. The probability a vehicle was made by Company A, given it was a car is (Round to three decimal places as needed.)The vast majority of European vehicles sold in the world (BMW, Audi, Mercedes- Benz, etc...) receive their transmissions from either ZF Friedrichshafen AG or Continental AG. After the acquisition of TRW by ZF, ZF AG supplied 69% of transmissions, and Continental AG supplied 31%. If three European cars are randomly selected, what is the probability that 2 of the cars use ZF transmissions and 1 use Continental AG transmission? Enter your answer in percent terms (for example 12.5% must be entered as 12.5).If a person randomly picks and buys one of the four newsletters in the street each morning. What is the probability that the person will purchase three different newsletters on three consecutive mornings?
- A survey found that 40% of Dynamic Housing’s potential customers viewed the single-family house virtual tours and of those that viewed the virtual tours 3% leased a single-family house. What is the probability that a potential customer will view the virtual tour and lease a single-family house.A manufacturer makes two models of an item: model I, which accounts for 75% of unit sales, and model II, which accounts for 25% of unit sales. Because of defects, the manufacturer has to replace (or exchange) 5% of its model I and 10% of its model II. If a model is selected at random, find the probability that it will be defective. Please round the final answer to 2 or 3 decimal places. P(detective)=On Monday and Wednesday night, Raymond went to bed listening to music on his phone. The phone contains music from 3 different composers. 5 songs are Palestrina, 1 song is Bach and 4 songs are Beethoven. His phone plays music in a random order. What is the probability that on both nights Raymond fell asleep listening to the same composer?