Circuit boards are assembled by selecting 4 computer chips at random from a large batch of chips. in this batch of chips, 90 percent of the chips are acceptable. let x denote the number of acceptable chips out of a sample of 4 chips from this batch. what is the least probable value of x?

the least probable value of X is X=0 , with probability P(X=0)=0.0001 =0.01%

Step-by-step explanation:

denoting X=number of acceptable chips out of a sample of 4 chips. If the probability of choosing one acceptable chip is 0.90 , then the probability of choosing one chip with failures is 1-0.90 = 0.1

since is less likely to take one failed chip ( 0.1 is smaller than 0.9) , and each chip is independent from the others , the least probable value of X is when there are 4 failed chips or 0 acceptable chips. then the probability for P(X=0) will be

P(X=0) = 0.1*0.1*0.1*0.1 = 0.0001

Note:

Strictly speaking , X has a binomial distribution , therefore

P(X) =  4!/[(4-x)!*x!]*0.9^x *0.1^(4-x)

that has a minimum value for X=0 → P(X=0)= 0.0001

Answer and explanation:

Geometary software is merely a software implementation of solving the area of a triangle. Therefore geometry software employs all the methods used in coordinate algebra(manual) albeit behind the scenes, in the console of the software, and just displays the area in the screen after solving. While geometry software displays the area using automated methods in code, coordinate algebra solves area of the triangle manually using several steps. In both cases, we observe that algebra is required to solve area of the triangle as it is part of the algorithm used in the code for the geometry software. Also being able to use the geometry software requires that one understand coordinate algebra to be able to plot lines, points and planes at the correct locations on the screen and get desired result.