Autism In recent years it was thought that approximately 1...

Name: Autism In recent years it was thought that approximately 1 in 95 children exhibited some form of autism. The most recent CDC study concluded that the proportion may be as high as 1 in 80. If indeed these new figures are correct, choose 3 children at random and find these probabilities. Enter your answer as a fraction or a decimal rounded to three decimal places.
Uploaded: 2022-08-06T03:00:14-08:00
Duration: 7 min 38 s
Channel: Jen H
Description: Autism In recent years it was thought that approximately 1 in 95 children exhibited some form of autism. The most recent CDC study concluded that the proportion may be as high as 1 in 80. If indeed these new figures are correct, choose 3 children at random and find these probabilities. Enter your answer as a fraction or a decimal rounded to three decimal places.

Autism In recent years it was thought that approximately 1 in 95 children exhibited some form of autism. The most recent CDC study concluded that the proportion may be as high as 1 in 80. If indeed these new figures are correct, choose 3 children at random and find these probabilities. Enter your answer as a fraction or a decimal rounded to three decimal places.

Transcript

00:01 Okay, so in this question, we're talking about autism, and i believe you accidentally left off part of the question, but i was able to find it.

00:08 So if the numbers are slightly different, that might be why.

00:11 But so we're choosing three children at random, and we're trying to find the following probabilities.

00:17 We want to first find the probability that none have autism.

00:21 And keep in mind, it says if the new figures are correct.

00:25 So we're talking about 1 in 80 children having autism.

00:32 It's going to be 1 in 80.

00:36 Let's go ahead and get that probability.

00:42 You just have to do 1 divided by 80 in your calculator.

01:00 So, well, i guess we didn't need to do that quite yet, but that's fine.

01:04 So we're going to have three students that we're picking.

01:10 So if the first student does not have autism, it's going to be 79 out of 80 is the probability, because it's only 1 in 80 that does times.

01:22 And also if the second one doesn't have it, 79 over 80 times 79 over 80.

01:36 So that's going to be a pretty high probability.

01:40 Now we're going to multiply this in our calculator, 79 times 79 times 79, divided by 80, divided by 80, divided by 80.

01:49 And you get 0 .96.

01:57 Three zero if you round.

01:59 So about 96 % chance that if you were to randomly select three children that none of them had autism.

02:06 Okay, now for the next question, we can't really calculate that as easily.

02:10 Let me just give some space here.

02:12 First of all, it's important to know that this follows a binomial distribution simply because autism you would either have it or not have it.

02:21 So it's just, that's how binomial distributions work.

02:25 It's either it's like on, off, yes, no type thing.

02:29 So we can use the formula here for finding the probability that exactly one child has autism.

02:42 So that's p of x equaling one.

02:49 And the formula for that, let me just go ahead and write the formula and then we'll fill in the values is n choose x times p to the x, q to the n minus x.

03:05 So x is the number of children that have autism.

03:12 P is the probability that that child will have autism, and q is the probability that they won't.

03:19 So here, n, we're looking at how many total students do we have, or children, three, and we're trying to see probability that one of them is going to have autism.

03:30 Probability that they have autism is 0 .0125.

03:40 And that's going to be to the first power times.

03:43 And we want to do the probability q that they will not have autism.

03:47 That's 1 minus .0125...

Question

Please give Ace some feedback