The probability that a tennis set will go to a tie-breaker is 19%. what is the probability that two of three sets will go to tie-breakers?

The probability is:

0.087723

Step-by-step explanation:

We need to use the binomial distribution to calculate the probability.

We are given that:

The probability that a tennis set will go to a tie-breaker is 19%.

i.e. the probability is: 0.19

Also, we are asked to find  the probability that two of three sets will go to tie-breakers.

We know that the probability of binomial distribution is given as:

where n are the total outcomes.

p is the probability of success.

and P denotes the probability.

Here we have:

p=0.19

k=2

and n=3

Hence,

Hence, the probability that two of three sets will go a tie breaker is:

0.087723

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

idk this answer sorry cant on this one.

step-by-step explanation: