Pottery An artist experimenting with clay to create pot-tery with a special texture has been experiencing dif-ficulty with these special pieces. About 40% break in the kiln during firing. Hoping to solve this problem, she buyssome more expensive clay from another supplier. Sheplans to make and fire 10 pieces and will decide to usethe new clay if at most one of them breaks.a) Suppose the new, expensive clay really is no betterthan her usual clay. What’s the probability that this testconvinces her to use it anyway? (Hint: Use a Binomialmodel.)b) If she decides to switch to the new clay and it is nobetter, what kind of error did she commit?c) If the new clay really can reduce breakage to only20%, what’s the probability that her test will not detectthe improvement?d) How can she improve the power of her test? Offer atleast two suggestions.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
tery with a special texture has been experiencing dif-
ficulty with these special pieces. About 40% break in the
some more expensive clay from another supplier. She
plans to make and fire 10 pieces and will decide to use
the new clay if at most one of them breaks.
a) Suppose the new, expensive clay really is no better
than her usual clay. What’s the
convinces her to use it anyway? (Hint: Use a Binomial
model.)
b) If she decides to switch to the new clay and it is no
better, what kind of error did she commit?
c) If the new clay really can reduce breakage to only
20%, what’s the probability that her test will not detect
the improvement?
d) How can she improve the power of her test? Offer at
least two suggestions.
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