Ten percent of the engines manufactured on an assembly line are defective. If engines are randomly selected one at a time and tested, what is the probability the fourth defective engine will be found on the second trial?

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Step-by-step explanation:

From the given information;

Let x be the number of trails on which the defective occurs.

Let the probability that an occurrence of a defective be p = 0.10

Suppose x is a random variable that follows a negative binomial distribution with parameters r and p.

Then the probability mass function of X can be expressed as:

We are to find the probability of the fourth defective engine will be found on the second trial.

i.e. r =  4 and x = 2

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.