A sample space S consists of five simple events with these...

A sample space S consists of five simple events with these probabilities. P(E1) = P(E2) = 0.15 P(E3) = 0.55 P(E4) = 2P(E5) (a) Find the probabilities for simple events E4 and E5. P(E4) = P(E5) = (b) Find the probabilities for these two events. A = {E1, E3, E4} B = {E2, E3} P(A) = P(B) = (c) List the simple events that are either in event A or event B or both. (If there are no simple events, enter NONE.) (d) List the simple events that are in both event A and event B. (If there are no simple events, enter NONE.)

Transcript

00:01 Hi, i'm david and i have you had a question.

00:03 Now let me pick up the question here.

00:06 In the question here we are going to discuss about the probability.

00:13 Now the first one in this question were given that the probability 1, it will equal to the probability of the e2, equal to the 0 .15, probability on the e3, it will equal to the z1, 55 probability that be 4 equal to 2 times probability that is 5 and the first time we need to do is we need to find the probability in 5 remember that it will end up the total probability under e9 it will equal to xan1 so this means then it will add up the probability 1 plus probability 2 plus probability e 3 plus probability the e 4 plus probability the e 5 it is exactly virtual 1 now e 1 equal to the 015 e 2 also equal to the 0 .15 e 3 equals 0 .15 5 e 4 equal to the 0 .15 e 4 equal to the 2 e5 and e5 equal to the 5 and e5 just equal to the n5 in the node and equal to 1 and then i will compute everything here and get equal to the 0 .3 plus 7 .55 equal to the 0 .85 equal to 1 and then this 2 here equal to the 3 probability the 5 so therefore we have the probability that e 5 equals to the 1 minus 025 is 1 in number 3.

02:01 Then we get the time from 2, 0 .05.

02:07 So from here we will see that the probability of the 4 equal to the 2, the property 05, equal to the 3 times 010 01, the 0 .05 equal to the 0 1 and the probability in 1 will equal to the 05 that will be done for the first part 8.

02:30 Now for the part b, want to find the probability for the two events.

02:38 We have the first event with the probability of the e1, e3 and e4.

02:49 So this will be the event a, poteer 1, e3, and e4.

03:02 So therefore, probability the a2, e4...

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