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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

Expert verified

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

Consider the set of all permutations of the numbers 1, 2, 3. If you select a permutationat random, what is the probability that the number 2 is in the middle position?In the first position? Do your answers suggest a simple way of answering the same questions for the set of all permutations of the numbers 1 to 7?

Suppose a coin is tossed three times. Let x be a random variable whose value is 1 if the number of heads is divisible by 3, and 0 otherwise. Set up the sample space for x and the associated probabilities. Find x and σ.

(a) Suppose you have two quarters and a dime in your left pocket and two dimes and three quarters in your right pocket. You select a pocket at random and from it a coin at random. What is the probability that it is a dime? (b) Let x be the amount of money you select. Find E(x).

(c) Suppose you selected a dime in (a). What is the probability that it came from your right pocket?

(d) Suppose you do not replace the dime, but select another coin which is also a dime. What is the probability that this second coin came from your right pocket?

A die is thrown 720 times.

(a) Find the probability that3comes up exactly 125 times.

(b) Find the probability that 3 comes up between115and 130 times.

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