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

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

a

step-by-step explanation: