Please explain to me how to solve the questions in detail.

Actually, I am preparing for my exam, but am unable to solve the problems.

16 Qs.8 : There are two candidates Ms. X & Ms. Y for the post of principal of a woman's college , whose chances of getting the post are in the ratio 8 : 2 . The chances that the co- education is introduced by the two candidates , if selected are 50% & 90% respectively If co -education is introduced by the new principal , find the probability that Ms, Y got the post . Qs 9. Three bags A, , A, . A, contain respectively 3 red , 4 white , I blue ; I red , 2 white , 3 blue ; 4 red , 3 white , 2 blue balls . One bag is chosen at random and a ball is withdrawn . It is found to be red . Find the probability that it comes from bag A, Qs. 10 : In a bolt factory machines A , B , C manufacture respectively 25 , 35 and 40 percent of the total .Out of their output 5 . 4 and 2 percent are defective bolts . A bolt is drawn at random from the produce and is found to be defective . What is the probability that it was manufactured by machine A ? Qs. 11 : In a lock producing factory , machines A , B , and Crespectively produce 250. 350 and 400 locks per day . Of their respective outputs 5% , 4% and 2% locks are defective . If a lock picked at random is found to be defective , find the probability that it was produced by Machine C Qs. 12 : There are three candidates X , Y , Z. for the post of Director of Institute , whose respective chances of getting the post are 50 % , 30% and 20 %. Their respective chances of introducing computers , if selected are 0.2 , 0.4 and 0.9 . If computers are introduced by the new director , what is the probability that Z has got the post ? Qs. 13 : In a multiple choice question with 4 alternatives . the probability of a candidate Ms. X knowing the correct alternative is 0.7 . If not , she makes a random guess. If she does the tick the correct alternative , what is the probability that she was guessing ? 2017 814 A husband and a wife appear in an interview for two vacancies and same post-. the probability of husband's selection is ly while the probability of wife's selection is 15. What is the probability that any one of them is selected 201 ) Q15. A problems in Mathematics is quien to three student A, B and C, whose thances of delving it are 1/, 1/'s and 1/4. What is the probability that the problem will be solved 2017 Q16 2 5 cards are drawn with replacement from a pack of card Find thi probability of the drawing atleast one shade Us. Explain mutual independence of three events E, Fand G. how that 4 EIF and G are random events in a sample space and if Eif and G are pair wise independent and E is independent ofQs. 1 (a) : Two dice are tossed 5 times . Find the probability of getting a sum of 7 atleast twice . Or If two dice are tossed 5 times , find the probability that a sum of 7 is obtained atleast twice . Qs. 1 (b) : Ten coins are thrown simultaneously . Find the probability of getting atleast seven heads . Qs . 1 (c) : Take 100 sets of 10 tosses of an unbiased coin . In how many cases do you expect to get 7 heads atleast ? Qs. 2 : A company has two projects at hand . The probability that Project A succeeds is 0,7 , that project B succeeds is 0.5 , and that both succeeds is 0.3 . Find the probability that 1 . atleast one succeeds. 2 . neither succeeds . Qs. 2( b) : The probability that A can solve the problem is 0.7 & the probability that B can solve the problem is 0.6 . Considering that these two events are independent , find the probability that the problem gets solved by either of them . Qs. 3 . If P(A) - 0.5 . P(B) = 0.7 and P( AnB) = 0.3 . find the probability that A occurs . given that B does not occur . BEL Eg 0 17 (1) S/ PLA) - 1/ 2 , PLBJ = 1/3 and PLANB) = 1/5. Their fund the probability that is Neither B occur (1 ) A occur but B does not Qs. 4 : A speaks the truth in 75 % and B in 80 % of the cases . In what percentage of occur cases are they likely to contradict each other in stating the same fact . (s 5 . If P(A) - 0.5 and P(A UB) = 0.6 , Find P(B) if 1. A and B are mutually exclusive 2. A and B are independent . 3. P(A | B) - 0.4 Qs. 6 : If the probability that an individual suffers a bad reaction from an injection is 0.001 . determine the probability that out of 2000 individuals ( based on Poissondistribution) 1 . exactly 3 2 . more than 2 individuals suffer a bad reaction . Qs. 7 : In a certain high school class consisting of 60 girls and 40 boys . it is observed that 24 girls and 16 boys wear eyeglasses . 1. What is the probability that a student picked at random wears eyeglasses , given that student is a boy ? 2. What is the probability that a student picked at random wears eyeglasses and is a girl ? 2019 &s. A class consists of 6 girls and 10 boys, If a committee of 3 BA PLOP is chosen at random from the class, find the probability that " exactly how boys are selected (i ) atleast one boy is selected (in) exactly two girls are selected.Qs. 4 : The mean & S.D of 9 observations was found to be 26.5 & 4 respectively . If an additional observation with value 40 is also included , calculate the new Mean and S.D. Qs. 5 : Obtain the mean and variance of the first n natural numbers