A machine makes errors in a certain operation with probability p. There are two types of errors. The fraction of errors that are type 1 is α, and type 2 is 1 - α.(a) What is the probability of k errors in n operations?(b) What is the probability of k1 type 1 errors in n operations?(c) What is the probability of k2 type 2 errors in n operations?(d) What is the joint probability of k1 and k2 type 1 and 2 errors, respectively, in n operations?

Step-by-step explanation:

The concept of binomial probability is applied.

Mathematically from binomial probability ; (nCx)px(1−p)(n-x)

The detailed step by step is as shown in the attachment

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step-by-step explanation:

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.