: 5 ٢:٥٦ quiz55.pdf → 5-1 / = Egbabl 1 dice In the experiment of throwing two far → let (A) be the event that the first die is add, (B) Be the event that second die is odd. PCB). the and - Fird the prob(A) = € التابخ O
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- The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)The conditional probability of E given that F occur is P(EF)= _____________. So in rolling a die the conditional probability of the event E. “getting a six,” given that the event F, “getting an even number.” has occurred is P(EF)= ____________.
- Spinner A and B shown in the figure are spun at the same time. (a) Are the events "spinner A stops on red” and “spinner B stops on yellow” independent? (b) Find the probability that spinner A stop on red and spinner B stops on yellow.An autonomous drilling rover is drilling and storing core samples to study the mineralcomposition of a new farming site. Under extreme heat, the drilling gear box has an operatingworking time of T ~ Γ(3, 1.2). When the drilling gear box fails, it is replaced by a new one. Whatis the probability that fewer than 3 drilling gear boxes fail at least in 1 day of drilling.The lung cancer hazard rate λ(t) of a t-year-old male smoker is such that λ(t) = 0.027 + 0.00025(t-40)2, and t >= 40. Assuming that a 40-year-old male smoker survives all other hazards, (a) what is the probability that he survives to age 50 without contracting lung cancer?(b) what is the probability that he survives to age 60 without contracting lung cancer?
- I ONLY NEED (D) (i) and (ii) answered please A fair die, with its faces numbered from 1 to 6, is one in which each number is equally likely to land face up when the die is rolled. On a fair die, the probability that the number 6 will land face up is 16. A group of students wanted to investigate a claim about manipulating a fair die so that it favors one outcome. The claim states that if a fair die is put into an oven and baked at 200°F for 10 minutes, the inside of the die will begin to melt. When the die cools, the inside will be solid again, but with more weight toward the bottom. This shift in weight will cause the face that was up when the die cooled to land up more often that the other faces. The students obtained a fair die and baked it according to the preceding directions. The die cooled with the number 6 face up. After the die cooled, they rolled the die 200 times, and the number 6 landed face up 43 times. Let p represent the population proportion of times the number 6 will…K1 IS GIVEN AS 0.58, FROM TABLE OF JOINT PMF ATTACHED TO THIS QUESTION, SOLVE THE FOLLOWING FOR RANDOM VARIABLES X & Y . -E[X]= -E[Y]= -Var[X]= -Var[Y] = -Cov[x,y] = - are x and y correlated ? explain your answerQ.2.1 It has been found that 1 out of every 10 visitors to a museum buys somethingfrom the gift shop. If we randomly select a sample of 12 visitors to themuseum, what is the probability that no more than three of the visitors willbuy something from the gift shop? Interpret your answer. Q.2.2 It has been found from experience that an exclusive clothes shop makes anaverage of four sales every fifteen minutes. If we randomly select a fifteenminute period, what is the probability that the shop will make: Q.2.2.1 More than one sale? Interpret your answer. Q.2.2.2 Less than three sales? Interpret your answer. Q.2.3 It has been found that the time taken to complete an emotional intelligencetest is normally distributed, with an average time (μ) of 18 minutes and astandard deviation (σ) of 3.5 minutes. What is the probability that a randomlyselected person will take: Q.2.3.1 Between 15 and 17 minutes to complete the test? Interpret youranswer.Q.2.3.2 More than 20 minutes to complete the test?…
- Between 5:00 pm and 6:00 pm, cars arrive at Jiffy Lube at the rate of 9 cars per hour (0.15 car per minute). This formula from probability can be used to determine the probability that a car will arrive within t minutes of 5:00 pm: F(t) = 1 - e-0.15t (a) Determine the probability that a car will arrive within 15 minutes of 5:00 pm (that is, before 5:15 pm).(b) Determine the probability that a car will arrive within 30 minutes of 5:00 pm (before 5:30 pm).(c) What value does F approach as t becomes unbounded in the positive direction?(d) Graph F using a graphing utility.(e) Using INTERSECT, determine how many minutes are needed for the probability to reach 60%.The life X (in years) of a voltage regulator of a car has the p.d.f. a) What is the probability that this regulator will last at least 7 years? (b) Given that it has lasted at least 7 years, what is the conditional probability that it will last another 3.5 years?T2.8 In testing of electric cables, the probability that any particular cable will be defective is .04. Let X be the number of defective cables found in a batch of 300 cables. Use normal approximation to the binomial distribution to find the probability that X is at most 20.