Question

In Problem, let A = {hand rests in last 10 minutes} and B = {hand rests in last 5 minutes}. Find P[B|A] for parts a, b, and c.

Problem

Consider Problem where the minute hand in a clock is spun. Suppose that we now note the minute at which the hand comes to rest.

(a) Suppose that the minute hand is very loose so the hand is equally likely to come to rest anywhere in the clock. What are the probabilities of the elementary events?

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(b) Now suppose that the minute hand is somewhat sticky and so the hand is 1/2 as likely to land in the second minute than in the first, 1/3 as likely to land in the third minute as in the first, and so on. What are the probabilities of the elementary events?

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(c) Now suppose that the minute hand is very sticky and so the hand is 1/2 as likely to land in the second minute than in the first, 1/2 as likely to land in the third minute as in the second, and so on. What are the probabilities of the elementary events?

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(d) Compare the probabilities that the hand lands in the last minute in parts a, b, and c.

The (loose) minute hand in a clock is spun hard and the hour at which the hand comes to rest is noted.

(a) What is the sample space?

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(b) Find the sets corresponding to the events: A = “hand is in first 4 hours”; B = “hand is between 2nd and 8th hours inclusive”; and D = “hand is in an odd hour.”

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(c) Find the events: A ⋂ B ⋂ D, Ac ⋂ B, A ⋃ (B ⋂ Dc), (A ⋃ B) ⋂ Dc.

Answer 1

A minute clock is spun and the point where it comes to rest is noted.

Let

,

.

The last 10 points on the clock are .

The last 5 points on the clock are .

So,

To find:

Use conditional formula,

a) Minute hand is equally likely to rest at any point on the clock:

b) The minute hand of the clock is sticky and is 1/2 as likely to land in the second minute than in the first, 1/3 as likely to land in the third minute as in the second and so on.

c) The minute hand is very sticky and so the hand is 1/2 as likely to land in the second minute than in the first, 1/2 as likely to land in the third minute as in the second and so on.