A shipment of 12 calculators has 4 that are defective if a...

A shipment of 12 calculators has 4 that are defective. If a random sample of 5 calculators is taken from this shipment, what is the probability that no more than 1 calculator is defective?

Transcript

00:01 In this video, our objective is to find out the probability that no more than one calculator is defective.

00:06 And again, one information we have is total number of calculator, which is n is equals to 12.

00:12 And number of defective calculators, number of defective calculators is equal to, which is denoted by x is equal to 5.

00:30 All right so now let's find out the probability of defective calculators from the given information so we will find out by this formula x upon n so which is equals to x is 4 and n is 12 that is equals to 0 .33 so now here we are assuming that let x denote the event or even selecting the calculator denote the event the selecting calculator all right so now x is the that means x is the binomial distribution with parameters n and p all right so here we are using the binomial distribution formula so probability mass function of binomial distribution is going to be equals to so we are using the usual formula to find out this then the formula is px is equals to n c x times px to the power p to the power x q to the power n minus x all right so now here p is the binomial probability x is the number of times for a specific outcome with n trials n c x is the number of combinations all right p is the probability of success on a single trial and q is the probability of failure on a single trial and n is the number of trials all right so here n c x is equal to n factorial upon x factorial times n minus x times factorial all right so the probability that no more than probability that no more than 1 calculator is defective is calculated as is equal to probability of x to be lesser than or equals to 1 is equal to probability of x is equal to 0 plus probability of x is equal to 1.

04:13 Now we have 2 values for x.

04:16 So let's put the values in the formula.

04:19 So 3, sorry, so 5c0 when probability of x is equal to 0 times 0 .33 to the power 0 times 1 minus 0 to 1 .33 to the power 5 minus 0...

Question

A shipment of 12 calculators has 4 that are defective. If a random sample of 5 calculators is taken from this shipment, what is the probability that no more than 1 calculator is defective?

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