The probability that a randomly selected box of a certain...

The probability that a randomly selected box of a certain type of cereal has a particular prize is 0.1. Suppose you purchase box after box until you have obtained four of these prizes. (a) What is the probability that you purchase x boxes that do not have the desired prize? nb(x; 4, 0.1) (b) What is the probability that you purchase six boxes? (Round your answer to four decimal places.) (c) What is the probability that you purchase at most six boxes? (Round your answer to four decimal places.) (d) How many boxes without the desired prize do you expect to purchase? How many boxes do you expect to purchase?

Transcript

00:01 So here the first question is we have to purchase x boxes that do not have the desired price.

00:07 P represents the purchase of x boxes do not have desired price.

00:14 And here it is given nb of x such that 410, nb of x such that 401, 0 .1, then h of x, that is nb, means negative binomial, h means hypergeometry function, 4, 110, another one is h of x such that 4 .0 .1 and binomial distribution, b represents binomial distribution.

00:47 So 4 .0 .1 and b of x comma 4 .1 .10.

00:54 Okay.

00:55 So now we are fixing the variable x as negative binomial distribution and the probability for that is p is equal to 0 .1 and based on the given question we can take r is equal to 4 so x follows negative binomial distribution okay so p is equal to 0 .1 and r is equal to 4 .4 .4.

01:19 R is equal to 4.

01:19 Therefore the corresponding the right option is this one n b negative binomial of x such that 4 comma 0 .1 that is r comma p okay so this is the right answer okay thank and we have three more subdivisions.

01:33 Then the question is probability of purchasing six boxes.

01:41 Okay.

01:42 So and we are selected, we will have only four sexes which means that in six boxes we will have four success and two failures.

01:54 So this is nb of two four zero point one.

01:59 So which is equal to the negative binomial distribution.

02:03 It is nb of.

02:05 Of x equal to x which is equal to x plus r minus 1 c r minus 1 p power or q power x so this is equal to 2 plus 4 minus 1 c 4 minus 1 into 0 .1 power 4 multiplied by 1 minus 0 .1 power 2 so which is equal to 5 c3 0 .1 power 4 into 0 .9 the whole square so upon simplification we will get this as 0 .2 the next question is p of p of p of p, probability of purchase of at most six boxes.

02:46 So here we have four success and two failures...

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