When a certain glaze is applied to a ceramic surface, the probability is 11% that there will be discoloration, 16% that there will be a crack, and 22% that there will be either discoloration or a crack, or both. Let X = 1 if there is discoloration, and let X = 0 otherwise. Let Y = 1 if there is a crack, and let Y = 0 otherwise. Let Z = 1 if there is either discoloration or a crack, or both, and let Z = 0 otherwise. Let pX denote the success probability for X. Find pX .

The value of pₓ is 0.11.

Step-by-step explanation:

The effects of a certain glaze on a ceramic surface are denoted as:

X = discoloration

Y = crack

Z = either discoloration or crack or both.

The success is denoted as 1 and failure as 0.

If X = 1 it implies that there is discoloration.

If X = 0 it implies that there is no discoloration.

The probability that there will be discoloration on applying a certain glaze is,

P (X = 1) = 0.11

Then the probability that there will be no discoloration is:

P (X = 0) = 1 - P (X = 1) = 1 - 0.11 = 0.89.

The variable pₓ denotes the success probability of random variable X.

In case of success the value of X is 1.

The probability of X = 1 is,

P (X = 1) = 0.11

Thus, the value of pₓ is 0.11.

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.