Question 3: PBS and the New York Times conducted a joint...

Question 3: PBS and the New York Times conducted a joint investigation of the credit card industry. They found that out of 145 million Americans with credit cards, 35 million pay only the minimum amount each month, 55 million pay more than the minimum but less than the full balance, and 55 million pay the full balance. Let A, B and C be the events that a randomly chosen credit card holder pays only the minimum amount, pays more than the minimum but less than the full balance, and pays the full balance, respectively. (a) Compute $P(A)$, $P(B)$, and $P(C)$. (b) Express \"the probability that a randomly chosen credit card holder who pays more than the minimum amount pays off his full balance\" in terms of A, B, and C, and compute this probability. [Hint: For any arbitrary events X and Y, $X \cap (Y \cup X) = X$ holds.]

Transcript

00:01 Now, let's solve this problem.

00:02 In this problem, mu value that is mean is given as mu and that will be n multiplied p.

00:08 So since this is a problem of binomial distribution, the n value will be my sample size which is given as 400 and p value is the probability of success which is given as 0 .30.

00:19 That is 30%.

00:20 So new comes out to be 120.

00:23 Right.

00:24 Now if i write the value of sigma, that is standard deviation, then it will be n multiplied p multiplied q so what is a value of q you is nothing but one minus p that is q is the you know probability of failure so okay so q is one minus p so i hope this value is known to you then if i just plug in the value like 400 multiplied 0 .3 0 multiplied 0 .70 then what will happen you will have your value for standard deviation as 9 .1 so, therefore, if i just go on and write that probability of x greater than equal to one one zero will be equals to one minus probability of x greater than or it will be probability of x less than.

01:17 So x less than or equal to 110.

01:21 Okay, so here what i have used is that, i have used this formula that if i have probability of x greater than a, then it is a.

01:29 Will be equals to 1 minus probability of x less than a okay so using this very concept i can write the value as for the above part okay so i'm just i'm particularly solving this this particular equation now the value will come around 1 minus probability of how much will be the value inside the bracket it will be x minus 120 over how much will it be at the denominator 1 9 .17 and then it will be less than equal to 1110 minus 120 over 9 .17.

02:06 Okay, right.

02:07 So, if you will solve it further, you can, you know, write this one as upon solving that this will be equals to and that z will be 1 .09 and then here it will be negative of 1 .0...

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