Joe is new to cooking the probability that joe burns dinner...

Joe is new to cooking. The probability that Joe burns dinner is 50%. (a) What is the probability that in the next dinners Joe prepares, 2 of them will burn? Express your answer as a decimal rounded to 4 decimal places after the decimal point. Answer: (b) What is the probability that in the next 5 dinners Joe prepares, at least 3 of them will burn? Express your answer as a decimal rounded to 4 decimal places after the decimal point. Answer: (c) What is the probability that in the next 5 dinners Joe prepares, less than 3 of them will burn? Express your answer as a decimal rounded to 4 decimal places after the decimal point.

Transcript

00:01 So joe's new to cooking and he burns his dinner 50 % of the time so the probability of burning is going to be 0 .5 so the probability of them not burning is also going to be 0 .5 so what is probability then in the next and i think it's going to be five dinners because everything else is five that two of them will burn but we don't know which two so we're going to take a combination of five picking in two at a time those two will burn so that's going to be 0 .5 the other three will not burn so that's going to be also at 0 .5 then we can go to our calculator and get that so we're going to go to b with the probability that at least three will burn that means we need to know the probability of three four and five so we need to find the probability of three plus probability of four plus the probability of five so that one we're going to have a combination of five picking three at a time so to reburn the other two do not we're going to have a combination of five picking four at a time those four burn the other one does not and then we're going to have a probability that the last one is just going to be 0 .5 to the fifth power because they're all are going to burn and then we would get that well again as a calculator, so let's go to see so what is the probability that less than three so that means the probability of zero one or two? we can simply go one minus the probability of three four and five so that's one minus the answer that we're going to get in part b so now let's go to our calculator here get the first one we're going to have a combination of five picking two at a time and then we're going to multiply that by 0 .5 times squared and 0 .5 to the third power that's going to be 0 .3 1 2 5 so now let's go get the next one 0 .5 picking three at a time and then we're going to get add that to a combination of five picking four at a time and i'm just doing all at once oops, time if i make sure i type it in right and then we're going to have the last one 0 .5 to the fifth power that's going to equal 2 .5...

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