Suppose a math class contains 35 students. There are 15 females (four of whom speak Spanish) and 20 males (five of whom speak Spanish). Give all answers as decimals to at least two decimal places.

Question

Suppose a math class contains 35 students. There are 15 females (four of whom speak Spanish) and 20 males (five of whom speak Spanish). Give all answers as decimals to at least two decimal places.

1. What is the probability that a randomly selected student speaks Spanish, given that the student is female?   

2. What is the probability that a randomly selected student does not speak Spanish, given that the student is male?   

3. What percent of Spanish speaking students are male? Give answer as a decimal.   

4. If someone does not speak Spanish what is the probability they are female?   

Answer 1

Hello Christy,

This is a math problem about probability. This can be an advance topic for elementary math. However, this is a very basic probability problem, and can be understood from our math knowledge about “percentage”, but none of probability theory. So take it easy.

Let’s solve a similar problem with some different numbers. After you learn the method you may easily solve the original math problem on your own. As for the answers to at least two decimal places, I will leave it for you, because when we reach to this probability level of math knowledge, that topic on decimal places is a know by default. In the case you do need further assistance on this part, let me know and I’d like to further help you.

So, here is our revised problem we are going to solve:

Suppose a math class contains 37 students. There are 21 females (six of whom speak Spanish) and 16 males (four of whom speak Spanish). Give all answers as decimals to at least two decimal places.

1. What is the probability that a randomly selected student speaks Spanish, given that the student is female?   

This question can be understood in two ways:

1) This is to ask about the percentage of students who are female Spanish speakers, or

2) This is to ask about the percentage of female students who are Spanish speakers.

Say we go with 1). We know there are total 37 students in the class. If we further know among all of our 37 students, how many of them are female who speaks Spanish, we then can just take the division.

The problem tells us that: There are 21 females (six of whom speak Spanish)

Hence, there are 6 female students speak Spanish.

Applying our division, we got 6/37. Calculation is left for you though.

Say we go with 2). The problem tells us, “There are 21 females (six of whom speak Spanish)”

This already tells us the answer, 6 of the 21 females speak Spanish, which gives us the answer 6/21 (simplify it).

2. What is the probability that a randomly selected student does not speak Spanish, given that the student is male?   

This question is closely similar to the first question. If you understand the first one, you can solve this one on your own.

3. What percent of Spanish speaking students are male? Give answer as a decimal.

To solve this percentage question, let’s first get clear on the asked percentage, it is about what to what.

The question states “What percent of Spanish speaking students are male?” Hence, it is about among all Spanish speaking students, what is the percentage of male students. Remember, percentage is just another way of division, a division resulted in a specific form of denominator of 100.

So, for our division, we would like to find out the number on the top (numerator), and the number at the bottom (denominator). For our natural thinking process though, it is easier for our brain to then think first about the denominator (which would give us a big picture of the problem), then look into the numerator (the specific of our big picture).

Alright, the big picture in this 3rd question is about all Spanish speakers. How many do we have in the class? The problem states “There are 21 females (six of whom speak Spanish) and 16 males (four of whom speak Spanish).” The info about Spanish speakers is given to us thru two pieces, both in the ( … ). Six females and four males speak Spanish. Hence we have total 10 students speak Spanish. This number 10 is our denominator.

Now, look into details about these 10 students. How many of them are male? The problem tells us that four of 16 males speak Spanish. Hence the number 4 is what we are looking for here. That is our numerator.

Hence, the asked percentage is 4/10 = 40/100 = 40%.

4. If someone does not speak Spanish what is the probability they are female?   

You can decompose this one just as we did in the 3rd one. Do you get an idea how to proceed?

To sum, this seems a math problem trying to introduce the basic idea on probability. It is a very nice problem to help you to gain a sense about what probability is about.

Let me know if further assistance is needed. Good study!

Answer 2

P(f)=15/35= 3/7

P(m)=4/7

P(s)=9/35

P(~s)= 26/35

P(~s/f)=11/15

1) P(s/f)=4/15 = 26.666..= about 26.67.% chance spanish speaking if female

3) P(s/m)=5/20=1/4=.25 =25% spanish speaking if male

2) P(~s/m)= 3/4 = 75% non-spanish speaking if male

4) P(f/~s)= probability a female if not spanish speaking

use Bayes Theorem or a venn diagram

bayes theorem is P(A/B)(P(B)=P(B/A)P(A)

replace A with f, B with ~s,

P(f/~s)f(~s) = P(~s/f)P(f)

P(f/~s) = (11/15)(15/35)/(26/35)=11/26

= about 42.31% chance female if not spanish speaking