Be A, BY C, three events associated with the same experiment. Suppose they meet the following conditions: P(4) =D 글, P(B) 3D 3, P(C) = , P(ANB) = }, P(AnC) = } y P(BnC) = . 1 1 Р(B) 1 y P(BnC) = 0 6 Calculate P (An (BUC)
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- 5. A candy dish contains 2 red (R) and 4 yellow (Y) candies. You close your eyes, select two candies from the dish (without replacement), and record their colors. Use general multiplication rule and special addition rule to find the following probabilities. a. The probability that the first selected candy will be red and the second selected candy will be yellow is b. The probability that two selected candies will be of different colors_ One is red, another one is yellow c. Probability that two selected candies will be of the same color_ Both are red or both are yellow Assuming that the event "The first selected candy will be red and the second selected candy will be yellow "is denoted by A, the event "Two selected candies will be of different colors" is denoted by B, and the event "Two selected candies will be of the same color" is denoted by C, show your work in finding P(A), P(B), and P(C) in the questions a, b, and c.Suppose there are 6 red balls and 4 white balls in a urn.(1) event A={First draw is a white ball}, what is P(A), probability of A?(2) Now assume we do picking balls one by one without replacement. event B={Second draw is a white ball}, what is P(B), probability of B? (3) Are A and B independent? Justify your answer. please explain and do all the steps fully!There are two bags containing several colored balls. The bag B, contains 10 red balls, 12 blue balls, and 13 green balls. The bag B, contains 20 red balls, 19 blue balls and 19 green balls. A student of your class wanted to draw 1 red ball and 3 blue balls. i. If he has the option to draw from only bag B1, what is the probability of drawing the four balls? [Give your answer upto 4 decimal places] ii. If he can choose any bag in an equiprobable manner, what is the probability of drawing the four balls in this case? [Give your answer upto decimal places] 4
- Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 43 passengers, and a flight has fuel and baggage that allows for a total passenger load of 7,181 Ib. The pilot 7,181 lb sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than - = 167 Ib. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an 43 overloaded aircraft? Assume that weights of men are normally distributed with a mean of 178.9 lb and a standard deviation of 35.4. The probability is approximately (Round to four decimal places as needed.)Consider two mutually exclusive events A and B such that P((A or B)^c)=4/7 and P(B)=1/7. Then P(A^C) is equal to Note: P(A^C) means probability of A complement О РАor B)+P(A) ЗР(В)+0.5 O P(B^C) O 2P(A)Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.46, P(F^) = 0.65, and P(E U F) =0.7. Calculate the probabilities below. (a) P(E) = (b) P(F) (c) P(E n F) =
- Q4) ( / In a laboratory two types of tests done for a concrete cubes: compression streng.h test and water absorption test .40% passed in compression test. 20% failed in water absorption test and 12% failed in both. Find: 1) the probability that a random sample selected is bad in compression test and good in absorption test. 2) the probability that a random sample selected is bad in absorption test and good in compression test. 3) the probability that a random sample selected is good in both test. 4) the probability that a random sample selected at least one of them is bad.Are couples that live together before they get married just as likely to end up divorced within five years of marriage compared to couples that live apart before they get married? 268 of the 674 couples from the study who lived together before they got married were divorced within five years of marriage. 173 of the 405 couples from the study who lived apart before they got married were divorced within five years of marriage. What can be concluded at the = 0.05 level of significance? For this study, we should use Select an answer z-test for a population proportion t-test for a population mean t-test for the difference between two independent population means z-test for the difference between two population proportions t-test for the difference between two dependent population means The null and alternative hypotheses would be: Select an answer μ1 p1 Select an answer ≠ > < = Select an answer p2 μ2 Select an answer μ1 p1 Select an answer < = > ≠ Select…
