There are five oklahoma state officials: governor (g), lieutenant governer (l), secretary of state (s), attorney general (a), and treasurer (t). take all possible samples without replacement of size 3 that can be obtained from the population of five officials. (note, there are 10 possible samples! )
(a) what is the probability that the governor is included in the sample?
(b) what is the probability that the governor and the attorney general are included in the sample?

a) 0.6

b) 0.3

Step-by-step explanation:

Since we are taking 3 from a sample of 5 without replacements, we would have 5 choices for the first pick, 4 choices for the 2nd pick and 3 choices for the 3rd pick. The total possible number of ways to do this is:

5*4*3 = 60 ways

As order does not matter (GLS is the same as GSL), we divide this by the number of ways the 3 picks can be arrange, which is 3*2*1 = 6

So there are 60/6 = 10 possible samples

(a) If the governor is included in the sample, then we only have 4 choices for the 2nd pick and 3 choices for the 3rd pick. And there are also 2 ways to arrange this.

So there are 4*3/2 = 6 possible samples. The probability of this happening is 6/10 = 0.6

(b) If G and A are included, we only have 3 choices for the last pick. So the probability of this to happen is 3/10 = 0.3

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

560

hope this : )