Suppose that all of the outcomes of a random variable are {a, b, c, d, e } , and that P(a)=P(b)=P(c)=P(d)= 1/4, (that is, all outcomes a, b, c, and d each have a 1/4 probability of occurring), and P(e)=0. Define the events A = (a, b), B= (b,c), C= (c, d}, and D= {e }. Calculate the probability P(A C). O 1/2 O 1/8 0 0 O 1/3Suppose that all of the outcomes of a random variable are {a, b, c, d, e }, and that P(a)=P(b)=P(c)=P(d)= 1/4, (that is, all outcomes a, b, c, and d each have a 1/4 probability of occuring), and P(e)=0. Define the events A = (a, b), B=(b,c}, C= (c,d}, and D=(e } . True or false: The events A and B are independent. . True O FalseSuppose that you have a loaded die. where the probability of landing on each number is given by the following: Find the standard deviation of a single roll of the die. ' 2.05 04.25 ' 1.05 ' 3.5 Suppose that you have e loaded die. where the probability of landing on each number is given by the following: Find the expected value of a single roll of the die. '1 '21 '15 '3 Suppose that the probabilities of events A and B are P(A)=.4, and P(B)=.5. If A and B are independent events, then P(B|A) is equal to O .4 O . 5 0 0 O Cannot be determined