Na school of 1250 students, 250 are freshmen and 150 students take spanish. the probability that a student takes spanish given that he/she is a freshman is 30%. are being a freshman and taking spanish independent?

No, being a freshman and taking Spanish are not independent.

Let A denote the event that the student is a freshman.

B denote the event that the student is taking Spanish.

Let A∩B denote the event that the the student is a freshman and takes Spanish.

Let P denote the probability of an event.

Now we know that:

Two events A and B are said to be independent if:

Also, in such a condition we have:

Now here we have:

Also we are given,

( Since, we are given  The probability that a student takes Spanish given that he/she is a freshman is 30% )

As we see that:

Hence, being a freshman and taking Spanish are not independent.

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation: