Animal 12. FIGURE 4.21 An eight-armed maze. bo. boAhiano (a) P[X< 3]. = 5 t (b) P[34]. (d) P[X = 4]. 53. Although errors are likely when taking measurements from photographic im- ages, these errors are often very small. For sharp images with negligible dis- tortion, errors in measuring distances are often no larger than .0004 inch. Assume that the probability of a serious measurement error is .05. A series of ` 150 independent measurements are made. Let X denote the number of serious 220Briva errors made. (a) In finding the probability of making at least one serious error, is the nor- mal approximation appropriate? If so, approximate the probability using this method. (b) Approximate the probability that at most three serious errors will be, made. 54. A chemical reaction is run in which the usual yield is 70%. A new process has been devised that should improve the yield. Proponents of the new process claim that it produces better yields than the old process more than 90% of the time. The new process is tested 60 times. Let X denote the number of trials in which the yield exceeds 70%. (a) If the probability of an increased yield is .9, is the normal approximation appropriate? (b) If p = .9, what is E[X]? (e) If n>.9 as claimed, then, on the average, more than 54 of every 60 trials will result in an increased yield. Let us agree to accept the claim if X is at %3D
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.
Tree diagram
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.
#53 please
![Animal
12.
FIGURE 4.21
An eight-armed maze.
bo.
boAhiano
(a) P[X< 3]. = 5 t
(b) P[3<X<6].
(c) P[X>4].
(d) P[X = 4].
53. Although errors are likely when taking measurements from photographic im-
ages, these errors are often very small. For sharp images with negligible dis-
tortion, errors in measuring distances are often no larger than .0004 inch.
Assume that the probability of a serious measurement error is .05. A series of `
150 independent measurements are made. Let X denote the number of serious
220Briva
errors made.
(a) In finding the probability of making at least one serious error, is the nor-
mal approximation appropriate? If so, approximate the probability using
this method.
(b) Approximate the probability that at most three serious errors will be,
made.
54. A chemical reaction is run in which the usual yield is 70%. A new process has
been devised that should improve the yield. Proponents of the new process
claim that it produces better yields than the old process more than 90% of the
time. The new process is tested 60 times. Let X denote the number of trials in
which the yield exceeds 70%.
(a) If the probability of an increased yield is .9, is the normal approximation
appropriate?
(b) If p = .9, what is E[X]?
(e) If n>.9 as claimed, then, on the average, more than 54 of every 60 trials
will result in an increased yield. Let us agree to accept the claim if X is at
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc074fc7e-4e48-46f1-bfc4-aee6ba4e6262%2F45eb8bc7-463f-4719-9b2a-94175b619739%2Ffaqx32l.jpeg&w=3840&q=75)
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