Answered: The probability of a defective GPS…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.8: Probabilities Of Disjoint And Overlapping Events

Problem 2C

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Related questions

Question

The probability of a defective GPS dropsonde is 0.008. You purchased 20 such sondes
for a field experiment and plan to make 10 launches during the experiment.
(a) What is the probability that 10 out of the 20 purchased sondes are bad?
(b) Now you picked 12 of the sondes and shipped them to the experiment site. What is
the probability that at least 10 of the sondes are in good quality?
(c) On your very first launch, you found the sonde you picked is a bad one. You replaced
it with another sonde, only to find that it was also defective. What is the probability for
this to happen?
(d) If indeed 5 out of the 20 purchased sondes are bad, what is the probability that all the
bad sondes are in the package you shipped to the experiment site?

Expert Solution

Step 1

In this case, each selected GPS drop sonde has the only options of being "defective" (defined as success) or "non-defective" (defined as failure). For a considered no. of GPS dropsonde (i.e., the no. of trails, $n < \infty$ ), with a specified probability of being defective (i.e., the prob. of success $p$ is fixed for each trail), the random variable " $X$ =no. of defective GPS dropsonde" is assumed to follow Binomial distribution. For $X ~ B (n, p)$ , the pmf is given as:

$P (X = x) = \{\begin{cases} ^{n} C_{x} p^{x} {(1 - p)}^{n - x}; x = 0, 1, 2, . . ., n \\ 0; O t h e r w i s e \end{cases}$