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Chapter 15: Q11P (page 728)

Set up several non-uniform sample spaces for the problem of three tosses of a coin

Short Answer

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The non-uniform sample space are 2t鈥�,1t鈥�,0tand0鈥�t鈥�,Atleast鈥�1鈥�t ,

Step by step solution

01

Definition of Non-Uniform Sample Space 

Non-Uniform Sample space of any experiment is the set of all possible mutually exclusive events such that each point has different probability to occur

02

Creation ofsample space for experiment toss of three coins

When three coins are tossed, with each toss there is a possibility of getting head or tail. The sample space is expressed as follows,

hhh,hht,hth,htt,thh,tht,tth,ttt

It has 8 events to occur.

Let the event be number of tails when three coins are tossed. The sample space will be and the point has probability14 12,and 14respectively and so, it is non-uniform sample space.

The sample space for no tail and at least 1 tail is ,and the point has probability 14and34 respectively and thus it is non-uniform sample space.

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Most popular questions from this chapter

A trick deck of cards is printed with the hearts and diamonds black, and the spades and clubs red. A card is chosen at random from this deck (after it is shuffled). Find the probability that it is either a red card or the queen of hearts. That it is either a red face card or a club. That it is either a red ace or a diamond.

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鈭�y,鈥夆赌�x/y,鈥夆赌�x2y3and .yln(x)

Prove (3.1) for a nonuniform sample space. Hints: Remember that the probability of an event is the sum of the probabilities of the sample points favorable to it. Using Figure 3.1, let the points in A but not in AB have probabilities p1, p2, ... pn, the points in have probabilities pn+1, pn+2, .... + pn+k, and the points in B but not in AB have probabilities pn+k+1, pn+k+2, ....pn+k+l. Find each of the probabilities in (3.1) in terms of the 鈥檚 and show that you then have an identity.

Set up an appropriate sample space for each of Problems 1.1 to 1.10 and use itto solve the problem. Use either a uniform or non-uniform sample space or try both.

A letter is selected at random from the alphabet. What is the probability that it is one of the letters in the word 鈥減robability?鈥� What is the probability that it occurs in the first half of the alphabet? What is the probability that it is a letter after x?

Do Problem 15for 2particles in 2 boxes. Using the model discussed in Example role="math" localid="1654939679672" 5, find the probability of each of the three sample points in the Bose-Einstein case. (You should find that each has probabilityrole="math" localid="1654939665414" 13, that is, they are equally probable.)
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