Sstasi runs out of time while taking a multiple choice test...

Name: sstasi runs out of time while taking a multiple choice test and plans to guess on the last 6 questions each question has 5 possible choices exactly one of which is correct let y denote the n 73517
Uploaded: 2021-10-17T15:56:50-08:00
Duration: 6 min 57 s
Channel: David Nguyen
Description: sstasi runs out of time while taking a multiple choice test and plans to guess on the last 6 questions each question has 5 possible choices exactly one of which is correct let y denote the n 73517

SStasi runs out of time while taking a multiple-choice test and plans to guess on the last 6 questions. Each question has 5 possible choices, exactly one of which is correct. Let Y denote the number of questions that she guesses correctly among the 6 questions. Determine P(Y=2).Based on the context of the previous question, determine P(Y>2).Based on the context of the previous question, determine expected value of Y.

Transcript

00:01 Hi, i'm david and i'm here to have you answering your question.

00:04 Let me bring up your question here.

00:06 In this question we recall about the binomial distribution.

00:10 If x followed by the binomial with the a and the p, and then the probability x equal to k, equal to n choose k, p power k, 1 minus p power n minus k.

00:24 And now in this question we are given a midterm test has four multiple choices.

00:30 With four choices and one correct answer each.

00:35 Now in this case means that we will have n equal to four questions and the probability of correct here it will equal to one out of four and then if we can x it will be the number of the correct and then x just follow the binomial with the n equal to four b equal to one over 4.

01:01 Now in the part a we want to find probability that you get exactly two questions correct.

01:08 So it means that probability x2.

01:11 Applying the formula here we should get will be 4 choose 2 and then p will be 1 out of 4 power 2.

01:20 1 minus 1 of the 4 will be 3 out of 4 power 2.

01:24 If we do this 1, 4 2 times 0.

01:31 25 power 2 times 0 .75 power 2.

01:37 Then we get equal to the 0 .0 .9, 375.

01:43 That's going to be the answer for the a.

01:46 And now, i'll assume that if you answer the question correct, you get the, so if you got the correct, you will have plus 5 points.

01:58 If you answer wrong, you have 2 minus 2.

02:02 Point and we call x will be the total the number of points so we want to know the probability mass function of the x now first we need to know how many value x can take here so i will call this one will be the y now because that will be the uh yeah i mean i don't want to confuse with the x here so this will be the y to make it easier now for the first case if we are not it will assume that we will have found 4 correct so c c c c c and then the second case we can have the one correct and three wrong and then so this only write this just the 4 correct and the next one i will have the two correct and two wrong the next one i have the three correct this one will be four correct three let me make in the right order so this one will be 3 correct and 1 wrong 4, 3, 2, this will be 1 correct and 3 wrong and the last one will be 0 correct and 4 wrong and therefore it will have 4 correct and then the value of the y it will equal to 4 times 5 will be 20 if we have 3 correct it will be 15 minus 2 will be 13 2 correct 2 correct will be 10, 10 minus 4 will be 6...

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