A coin will be tossed 100 times. You get to pick 11 numbers. If the number of he

elchatosarapage

elchatosarapage

Answered question

2021-11-09

A coin will be tossed 100 times. You get to pick 11 numbers. If the number of heads turns out to equal one of your 11 numbers, you win a dollar. Which 11 numbers should you pick, and what is your chance (approximately) of winning? Explain.

Answer & Explanation

Florence Pittman

Florence Pittman

Beginner2021-11-10Added 15 answers

Let 0 represent tails and let 1 represent heads. 
The 100 tosses are equivalent to drawing 100 tickets at random from a box that contains one ticket with the number 1 and one ticket with the number 0, since we have a 1 in 2 chance of getting heads. 
Numbers of draws=100 
Expected value and standard deviation of box 
The total value of all the tickets divided by the total number of tickets gives us the expected value of the box, which is the first thing we calculate. 
Expected value box =0+12=12=0.5 
Let us next determine the standard deviation using the shortcut formula: 
SD = (big number - small number ) ×fraction with big number×fraction wit small number 
=(10)×12×12 
=1×14 
=12 
=0.5 
Expected value and standard error of sum 
Next, the expected values for the sum is the product of the number of draws: 
=50 
The standard error of the sum is the product of the square root of the number of draws and the standard deviation of the box 
=5 We note that our picked numbers are all within one standard error of the expected value. The chance of winning is the area corresponding to z=1.00 in the normal probability table in the appendix, which is thus 68.27%

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