The failure rate for taking the bar exam in Philadelphia is...

The failure rate for taking the bar exam in Philadelphia is 40%. If a sample of 12 people who have taken the bar exam is selected, what is the probability? a) At least 2 people passed the exam. b) Exactly 3 people have failed the exam.(use the binomial formula) c) At least 10 people have failed.

Transcript

00:01 All right, so the question here says that the failure rate for taking the bar exam in philadelphia is 40%.

00:07 So if a sample of 12 people who have taken the bar exam is selected, so here we have to compute the probability.

00:14 So here the probability of success is 0 .40, right? now here we consider that x is a random variable representing the number of people who have failed out.

00:24 And this has binomial distribution for parameters that is sample size is 12.

00:30 Probability of success is 0 .40 right now here the probability mass function of x this is given as n c x into p to the power x into 1 minus p to the power n minus x now in the first part we have been asked that what is the probability that at least two people passed the exam that is probability of x is rather than equal to 2 right or we can say uh this is 1 minus the probability of is less than 2 so this is one minus probability of x is equal to 0 plus probability of x is equal to 1 right so this is 1 minus 12 c 0 into 0 .4 to the power 0 into 0 .6 to the power 12 minus 0 plus 12 c1 into 0 .4 to the power 1 into 0 .6 to the power 1 into 0 .6 to the power 12 minus 1 right so here this probability is computed as 0 .997 right the next part of the question is to determine the probability that exactly three people have failed the exam so in this case we have to determine the probability so here we have the failure rate right so okay okay so in the previous part basically we have to determine the probability for the passing right so okay so here basically this will probability that at least two people have passed so this will be equal to one minus the probability that the less than two people have passed so in this case the probability of success will be one minus 0 .4 that is 0 .6 right so we'll use the same formula just the probability of success will change and the answer computed here is 0 .997 right now in the next part we have been asked to determine the this is the probability that exactly three people have failed that is probability for x is equal to three so this is equal to 12c3 into 0 .4 to the part 3 into 1 minus 0 .4 to the part 12 so this is equal to 0 .1419.

03:22 And for the last part of this question, we have to determine the probability that at least 10 people have failed.

03:28 That is probability of x is greater than equal to 10.

03:31 That is probability of x is 10 plus x is 11 plus x is 12...

Question

The failure rate for taking the bar exam in Philadelphia is 40%. If a sample of 12 people who have taken the bar exam is selected, what is the probability? a) At least 2 people passed the exam. b) Exactly 3 people have failed the exam.(use the binomial formula) c) At least 10 people have failed.

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