You are packing clothes for vacation and don’t want to take any button down shirts. You randomly choose three shirts from a jar containing three T-shirts, three polo shirts, and four button downs.

a) what is the probability that the first three shirts are button downs when you replace each shirt before choosing the next one?
b) what is the probability that the first three shirts are button downs when you do not replace each shirt before choosing the next one?

a) Because each pick is independent (we pick and then replace), we just have to find the probability of picking it out once, then cube that. This probability is 4/(3+3+4)=2/5. So, it is 8/125.

b) If we replace it, then we can do it in a strategic way:

The probability of picking it out the first time is 2/5. Now, there are 3 button downs and 9 shirts total.

The second time: 3/9=1/3

Now there are 2 and 8

Third time: 2/8=1/4.

The final probability is 2/5*1/3*1/4=1/30

step-by-step explanation:

use pothagarean therom

a^2+b^2=c^2 so first ac

acm is a right triangle because c= 90°

and am (the hypotenuse or c) =16+9 =25

but there is not enough info we need another angle or side length

1. sometimes

2. never true

3. sometimes

step-by-step explanation:

these are pretty self explanatory if you know what supp right and com angles are