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You select a marble without looking and then put it back. if you do this 12 times, what is the best prediction possible for the number of times you will pick a green or a white?

 

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

int myRandomNumber;

srand(time(NULL)); // seed the random number generator

myRandomNumber = rand(); // each time you call this function there will be a different random number.

Generate a random number, and output it. Use if statements to determine if the number is odd or even, and output a message to that effect. Similarly, output if the number is divisible by 3, and if it is divisible by 10. Use the % operator to achieve this. Run the program, and print the results several times using different numbers to be sure that it’s working.

People enter a restaurant and check their hat at the coat check, but since the worker is new, he makes the mistake of throwing all the hats in a pile. When the patrons return to claim their hats at the end of the evening, the worker gives each person a random hat from the pile.  

1. What is the probability that no one receives their own hat back if there are only 2guests?

2. What is the probability that no one receives their own hat back if there are 3 guests?

3. What is the probability that no one receives their own hat back if there are 4 guests?

4. What is the probability that no one receives their own hat back if there are 8 guests?

5.What is the probability that no one receives their own hat back if there are 10 guests?

To solve, build a systematic method. For example, one way you could do it is by defining several events, where P_i = the number of ways of a person i to recive their hat correctly, and then the number of ways that at least one person to recive their hat is the union of P_1,...,P_n; finally, you can count this using inclusion/exlusion, then count the complement to finish the problem. 

 

A deck of n cards numbered 1 through n is thoroughly shuffled so that all possible n! orderings can be assumed to be equally likely. Suppose you are to make n guesses sequentially, where the ith one is a guess of the card in position i. Let N denote ht number of correct guesses. (a) If you are not given any information about your earlier guesses show that, for any strategy, E[N]=1. (b) Suppose that after each guess you are shown the card that was in the position  in question. What do you think is the best strategy? Show that, under this strategy.

 

(c) Suppose that you are told after each guess whether you are right or or wrong. In this case, it can be shown that the strategy which maximizes  E[N] is one that keeps on guessing the same card until you are told you are correct and then changes to a new card. For this strategy, show that 

 

Hint: For all parts, express N as the sum of indicator Hint: For all parts, express N as the sum of the indicator.

 

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