Three balls are numbered 1, 2, 3 and placed in a bag. Consider the following experiment: two balls are chosen randomly without replacement from this bag. Let X¡ and X2 denote the number of the first and second ball, respectively. Define Y = |X1 – X2]. This experiment is repeated 50 times, the result of the i-th round is denoted by Y;. 50 Let Y50 = 1 Y;). What is the probability that Y50 will be different 50 (2Y: from E[Y;] by 0.05 or more? i. Use Chebyshev's Inequality. ii. Use Central Limit Theorem.

A test was given to a group of students. The grades and gender are summarized below   A B C Total Male 13 7 4 24 Female 12 17 9 38 Total 25 24 13 62 If one student is chosen at random from those who took the test,Find the probability that the student was female GIVEN they got an 'A'.

A test was given to a group of students. The grades and gender are summarized below   A B C Total Male 13 18 4 35 Female 5 3 11 19 Total 18 21 15 54 If one student is chosen at random from those who took the test,Find the probability that the student was female GIVEN they got a 'B'.

A test was given to a group of students. The grades and gender are summarized below A B с Total Male 5 4 2 11 Female 19 13 8 40 Total 24 17 10 51 If one student is chosen at random from those who took the test, Find the probability that the student got a 'C' GIVEN they are female.

A researcher is selecting lab rats for her experiment.  She assigns each rat a number and picks numbers out of a hat while blindfolded.  The pool of rats from which she is drawing participants is composed of the following: 23 male albino rats 21 male spotted rats 35 female albino rats 11 female  spotted rats If she reaches into the hat once, what is the probability of choosing a female rat or an albino rat? Give your answer as a decimal rounded to 4 decimal places.

A test was given to a group of students. The grades and gender are summarized below   A B C Total Male 2 15 3 20 Female 14 8 18 40 Total 16 23 21 60 If one student is chosen at random from those who took the test,Find the probability that the student was female GIVEN they got a 'A'.

A test was given to a group of students. The grades and gender are summarized below   A B C Total Male 5 2 9 16 Female 13 18 14 45 Total 18 20 23 61 If one student is chosen at random from those who took the test,Find the probability that the student got a 'A' GIVEN they are male.

A test was given to a group of students. The grades and gender are summarized below A B C Total Male 15 14 4 33 Female 7 19 13 39 Total 22 33 17 72 If one student is chosen at random from those who took the test, Find the probability that the student got a 'A' GIVEN they are female.