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bekas
1 month ago
3

A classic experiment in the 1960s eloquently illustrated the technical side of conservatism bias. The researchers presented subj

ects with two urns: one containing 3 blue balls and 7 red balls, the other containing 7 blue balls and 3 red ones. Subjects were given thisinformation and then told that someone had drawn randomly 12 timesfrom one of the urns [with replacement]. Subjects were told that thisdraw yielded 8 reds and 4 blues. They were then asked, "What is theprobability that the draw was made from the rst urn?" Formulate the problem in terms of Bayes' Rule. State all of your assumptions and all assignments explicitly.
Mathematics
1 answer:
Zina [12.3K]1 month ago
8 0

Answer:

Step-by-step explanation:

Urn I contains 3 blue balls and 7 red balls.

Urn II has 7 blue balls and 3 red balls.

When draws are made with replacement, the counts of red and blue will follow a binomial distribution with equal likelihood for each attempt.

Let B denote the outcome of drawing 8 reds and 4 blues.

A1 represents a draw from Urn I.

A2 corresponds to a draw from Urn II.

It is important to note that A1 and A2 are mutually exclusive and collectively exhaustive.

The probability we seek is P(A1/B) = \frac{P(A1B)}{P(A1B)+P(A2B)}

P(A1B) = (\frac{7}{10} )^8*(\frac{3}{10} )^4\\=\frac{7^8(3^4)}{10^{12} }

P(A2B) = (\frac{3}{10} )^8(\frac{7}{10} )^4\\=\frac{3^8(7^4)}{10^{12} }

P(A1/B) =\frac{7^8(3^4)}{7^8(3^4+3^8(7^4)}

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Answer:

Refer to the explanation

Step-by-step explanation:

As approximately 10% of users fail to close Windows properly, we determine:

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The missing graph has been provided.

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