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Chapter 15: Q23P (page 736)

A thick coin has probability 37of falling heads, 37of falling tails, and 17of standing one edge. Show that if it is tossed repeatedly it has probability 1 of

Eventually standing on edge.

Short Answer

Expert verified

Answer

The probability that the coin stands on the edge is 1.

Step by step solution

01

Given Information

A thick coin has probability 37of falling heads, 37of falling tails, and17 of standing on edge.

02

Definition of Independent Event

The events are said to be independent when the occurrence or non-occurrence of any event does not have any effect on the occurrence or non-occurrence of the other event.

03

Finding the probability that the coin lands on edge

The probability that the coin doesn’t land on edge is 67and when the toss is done -times, the probability of not falling on edge is 67n.

This implies that the probability of landing on edge at least one time is1-67n.

As the number of tosses increase the value of 67ngets closer to 0 and the probability eventually becomes 1.

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Most popular questions from this chapter

Given the measurements.

x:98,101,102,100,99y:21.2,20.8,18.1,20.3,19.6,20.4,19.5,20.1Find the mean value and the probable error of x−y,  x/y,  x2y3and .yln(x)

In paying a bill by mail, you want to put your check and the bill (with a returnaddress printed on it) into a window envelope so that the address shows right sideup and is not blocked by the check. If you put check and bill at random into theenvelope, what is the probability that the address shows correctly?

(a) Find the probability that in two tosses of a coin, one is heads and one tails. That in six tosses of a die, all six of the faces show up. That in12tosses of a12 -sided die, all12 faces show up. That in n tosses of an n-sided die, all n faces show up.

(b) The last problem in part (a) is equivalent to finding the probability that, when n balls are distributed at random into n boxes, each box contains exactly one ball. Show that for large n, this is approximatelye−n2πn.

Two cards are drawn at random from a shuffled deck and laid aside without beingexamined. Then a third card is drawn. Show that the probability that the thirdcard is a spade is ¼ just as it was for the first card. Hint: Consider all the (mutuallyexclusive) possibilities (two discarded cards spades, third card spade or not spade,etc.).

(a) Following the methods of Examples 3,4,5, show that the number of equally likely ways of putting N particles in n boxes,n>N, nNisfor Maxwell Boltzmann particles, C(n,N)for Fermi-Dirac particles, C(n−1+N,N)andfor Bose-Einstein particles.

(b) Show that if n is much larger than N (think, for example, ofn=106,N=10), then both the Bose-Einstein and the Fermi-Dirac results in part (a) contain products of N numbers, each number approximately equal to n. Thus show that for n N, both the BE and the FD results are approximately equal tonNN!which is1N!times the MB result.
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