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Numerade Educator



Problem 112 Hard Difficulty

identifies a group of children by one of four hair colors, and by type of hair.
$$\begin{array}{|l|l|l|l|}\hline \text { Hair Type } & {\text { Brown }} & {\text { Blond }} & {\text { Black }} & {\text { Red }} & {\text { Totals }} \\ \hline \text { wavy } & {20} & {} & {15} & {3} & {43} \\ \hline \text { Straight } & {80} & {15} \\ \hline \text { Totals } & {20} & {} & {} \\ \hline\end{array}$$
a. Complete the table.
b. What is the probability that a randomly selected child will have wavy hair?
c. What is the probability that a randomly selected child will have either brown or blond hair?
d. What is the probability that a randomly selected child will have wavy brown hair?
e. What is the probability that a randomly selected child will have red hair, given that he or she has straight hair?
f. If B is the event of a child having brown hair, find the probability of the complement of B.
g. In words, what does the complement of B represent?


a) answer not available
b) $\frac{43}{215}$
c) $\frac{120}{215}$
d) $\frac{20}{215}$
e) $\frac{12}{172}$
f) $\frac{115}{215}$
g) B complement will include those children who have blond, black or red color.


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Tiffany P.

April 2, 2021

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Video Transcript

Hi. We're looking at question 112 where they've identified a group of Children with hair color and type of hair and part A wants us to fill in the table. So we're gonna start with the easier ones and we can fill in the total for the brown by taking 20. 20 plus 80 equals 100. So 100 will go in that row and then, um, for the blonde, because we know our total is 20 and we know 15 of them have straight hair. What's leftover? Must be our wavy hair. So five would be a result there. Um, we can't fill in too much with the black hair from the column because we only have one number, but from the red hair weaken, do three plus 12 is 15. So now we have some options to fill in what's left. Um, the easiest thing it looks like to me to fill in the total for the black hair would be to take the total for the row, which is the 215. And we'll subtract the 15 from the red, the 20 from the blonde and the 100 from the brown which will give us a tea. So 80 is what goes in the column for the black. So then, to calculate the value for the straight black, we'll do a T minus 15 which is 65. So 65 will go right there and then we're only missing one thing. Now that's the total for the, um, straight hair. So we'll take 80 plus 15 close 65 plus 12 and and those up. Then we end up with 172. So 172 goes there. So that fills in our table, which is part a. And then we're going to be using those values to answer the remaining questions. And for this particular question, they just have the answers infraction for math. So I have to find the probability of wavy hair. We're just going to find the total number of students with wavy hair, which they actually gave us in the original part of the question. Just 43 out of the total number of students, which is 215 and in this case, the answer's air infraction form. So we don't need to divide it for brown or blond hair. We have to look at the totals in those two columns, so the total in the brown hair column is 100 and the total in the blood hair column is 20 that was given to us out of our 215 students. So that's 120 over to 15 and then wavy brown hair. So this one, we actually need to find the wavy row brown her column and where they need, which is it 20. And that's out of the 215 um, total students. So that's those three sections. Now we'll continue on and have red hair given straight hair. So this is one of those given questions where we need to consider what, um, what we're working out of. So we're looking on Lee in the straight hair row for any of our information because it's given that it's straight hair. We want the red hair in the straight hair rope, which is 12. And then again, we are only considering straight haired students, so that's gonna be 12 out of 1 72 So there's 12 students out of 172 students with straight hair, 12 of them have red hair, so that's our probability There for a part. F. They tell us that B is the event of a child having brown hair, and they want us to find the probability of that complement of Brown Will Complement is meeting. It's not brown, so it's a probably of not brown hair or probably, if not to be so for not brown hair that would include the red hair, the blonde hair and the black haired students. Or we can just say that, not brown hair students. So we could just take the total of 2 15 and subtract the 100 students with brown hair out of one's out of the 215 students that we have, So that would be 1 15 over to 15. Another way of doing that would be also to get the 1 15 would be to take the, um, 20 blonde haired students, plus the 80 black haired students, plus the 15 red haired students that would get us sustain number with the same answer. And then finally, it asks us to, um, find or two right, explain in words. It says, What does the compliment terms of b represent. So the V compliment will include anyone who doesn't have brown hair. So it will include Children with, um, long hair, red hair and black hair. And that's all there is to it. Thank you.