Question

You toss 3 coins. What is the probability that you get exactly 2 heads, given that you get at least one tail? A tree diagram will help you to answer this question.

There are 40 people at a reception for international students. The students, boys and girls, are from Peru and China. 18 of all the students are boys, and 12 of all the students are Peruvian. 17 of the Chinese are girls. Given that a student is a boy, what is the probability that he is Chinese? A Venn diagram will help you to answer this question.

Tests by an independent auditing firm show that 60% of students in a certain school think that Algebra is the best course they have ever taken. Use the entire line of random numbers below to estimate the probability that a randomly selected group of five students will contain at least 3 Algebra lovers. Let the digits 1-6 represent a student who thinks that Algebra is the best course.

12024 55976 61475 70726 25408 62279 71874 03499 92659 26041

Answer 1

help with 3 questions @Vocaloid

Answer 2

@Nnesha

Answer 3

@Vocaloid

Answer 4

For the first question, the answer is 3/7.

This is because of the varying possibilities.

One in which all are Tails
Three in which two are Heads
Three in which two are Tails
And then lastly,
One in which all are Heads

That gives us eight total possibilities. Since the question says that one is at least Tails, we exclude our last possibility (One in which all are Heads).

That leaves us with seven total possibilities, with three in which two coins are Heads.

And that's how we get 3/7.

Answer 5

For the second question, I can you setup a way to attack this question.

"There are 40 people at a reception for international students. The students, boys and girls, are from Peru and China."

We know we are working with 40 people, with some quantity of boys and girls, and some quantity of Peruvians and Chinese.

"18 of all the students are boys, and 12 of all the students are Peruvian. "17 of the Chinese are girls.""

This tells us that there are 18 boys. But also tells us that there are 22 girls. Given that 40 - 18 = 22. Total # of students minus # of boys equals # of girls. Also, 12 Peruvians.

We can obtain the total # of Chinese by subtracting the total # of Peruvians (12) from the total # of students (40) which is 28.

This is the key to solving our question, which is "Given that a student is a boy, what is the probability that he is Chinese?"

The question wants us to give # of Chinese boys over # of Chinese

We have the # of Chinese girls and the # of Chinese, so we can determine our # of Chinese boys.

Let x = # of Chinese boys

17 + x = 28
x = 11

Put # of Chinese boys over total # of Chinese

11/18 is your probability, given that a student is a boy, that he is Chinese.

Answer 6

Wow! That explains sooooooooooooooooo much =)))))))))))))))))

Answer 7

@Shadow Thank you

Answer 8

No problem

Answer 9

@Zarkon Can take the last one if he wishes.

Answer 10

help with the third =)

Answer 11

How many numbers in this group, 12024, are between 1 and 6 inclusive?

Answer 12

I'm not going to just give out a solution. If you answer my question I might be back.

Answer 13

5?

Answer 14

Im to late once again

Answer 15

@zarkon

Answer 16

@Shadow

Answer 17

????/

Answer 18

@theDeviliscoming @ThisGirlPretty

Answer 19

@Shadow :(

Answer 20

How many numbers in the set "12024" are 1-6

Answer 21

If you do not understand the question, let me know.

Answer 22

For clarification, we are thinking of each number in "12024" individually. Does 1 follow the rule 1-6? Yea or nay?

Answer 23

no?

Answer 24

Do you understand inequalities?

Answer 25

Less than, greater than, equal to, etc

Answer 26

Yes

Answer 27

:/

Answer 28

This is our rule.

\[1\le x \le 6\]

A number must be equal to 1, greater than one, equal to 6, or less than 6, in order to follow our rule. This is also essentially what 1-6 is saying.

Answer 29

When we look at "12024" we need to see if each number follows our rule.

Answer 30

okay so from that only two numbers are like that 12024 and 26041

Answer 31

am I correct? :/

Answer 32

Let me show you the first group, aka 12024

1 follows our rule, since it is equal to 1.
2 follows our rule, since it is between 1 and 6
0 does not follow our rule, as it is not equal to 1 or 6, and is not between 1 and 6.
2 and 4 likewise, follow our rule since they are between 1 and 6.

Answer 33

oh okay so each individual digit needs to apply to the rules

Answer 34

Yes

Answer 35

Do the second group for me.

Answer 36

55976

5 follows our rule, since it is less than 6.
5 follows our rule, since it is less than 6
9 does not follow our rule, as it is not equal to 1 or 6, and is not between 1 and 6.
6 follow our rule
7does not

Answer 37

Correct, so now lets look at all the groups.

12024 55976 61475 70726 25408 62279 71874 03499 92659 26041

Our question is "estimate the probability that a randomly selected group of five students will contain at least 3 Algebra lovers."

So we need to see out of these ten groups, which have at least three students out of the five who love Algebra.

If a number follows our rule, then it signifies a student that loves Algebra.

In our first group, 4/5 people love Algebra. In our second group, 3/5 people love Algebra.

So far, two groups out of ten fulfill our 3/5 criteria.

Answer 38

Do you see what we have to do now?

Answer 39

yes kind of

Answer 40

Check the remaining eight groups to see if they fit our 3/5 Algebra lover requirement.

Answer 41

61475

6-yes
1-yes
4-yes
7-no
5-yes

Answer 42

70726
7-no
0-no
7-no
2-yes
6-yes
25408
2-yes
5-yes
4-yes
0-no
8-no
62279
6-yes
2-yes
2-yes
7-no
9-no
71874
7-no
1-yes
8-no
7-no
4-yes
03499
0-no
3-yes
4-yes
9-no
9-no
92659
9-no
2-yes
6-yes
5-yes
9-no
26041
2-yes
6-yes
0-no
4-yes
1-yes

Answer 43

Now that we have that information gathered, lets array it like this. Does a group fit our criterion, Yea or Nay?

Group 1: Y
Group 2: Y
Group 3: Y
Group 4: N
Group 5: Y
Group 6: Y
Group 7: N
Group 8: N
Group 9: Y
Group 10: Y

Answer 44

That gives us 7 Y's and 3 N's

Answer 45

okay

Answer 46

7/3

Answer 47

?

Answer 48

Not quite. Remember, our question was essentially asking, if we were to pick a random group out of these ten, would it fit the criterion of at least 3/5 Algebra Lovers.

Answer 49

so yes

Answer 50

What is the probability that I will pick a ball of string out of this bowl, if my eyes were closed?

Answer 51

1/3

Answer 52

Correct

You put the total # of objects that fit the criterion over the total # of objects.

Answer 53

so it would just be 1/3

Answer 54

For this mini question, yes. But I wanted to see if this could help illustrate how to answer #3.

Remember,
# of groups that fit our criterion: 7
# of groups that do not fit our criterion: 3
total # of groups: 10

Answer 55

well we have to go with the one that does fit right we don't have anything to do with the one that doesn't fit

Answer 56

You are getting warmer.

Answer 57

7/10

Answer 58

Correct :)

Answer 59

thanks again

Answer 60

No problem.

To be safe, you can convert your fraction 7/10 into a percent.

Divide 7/10, get 0.7 or 70%.

Answer 61

Given the entire line of random numbers, you have a 70% of randomly selecting a group of five students that contain at least 3 Algebra lovers.

Answer 62

Thank ya