Probability, flipping a rigged coin problem

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In summary, the coin has a .52 probability of landing on heads and a .48 probability of landing on tails. When tossed three times, the probability of all heads is .1406. For the second scenario of 2 tails and a head in that order, the probability is .1198. This is because each flip of the coin has no bearing on the other flips, so the probabilities can be multiplied together.
  • #1
danielmcg90
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A coin is loaded so that the probabilities of heads is .52 and the probability of tails is .48.
If the coin is tossed 3 times what is probabilities that

a) all heads

b) 2 tails and a head in that order

I figured out part a). So i just thought of it with an and statement. ( I want heads and heads and heads) since the previous flip has no bearing on the next flip i can just multiply the quantities,

so P(all heads) = .52(.52)(.52) = .1406 which is the right answer

For part b) i am confused some how i have to implement that order is going to matter so I can just multiply them and that's it.
But still each flip of the coin has no bearing on the other flips so..
Can someone explain? the answer in the book is .1198
 
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  • #2
Why do you think you can't just multiply them like in the first case? You have three events occurring in a definite order with a definite probability for each.
 

What is probability?

Probability is the likelihood or chance of a particular event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

What is a rigged coin?

A rigged coin is a coin that has been altered or tampered with in some way to give a specific outcome when flipped. This could be done by adding weight to one side, shaving the edges, or using a magnet.

How do you calculate the probability of flipping a rigged coin?

The probability of flipping a rigged coin depends on the specific alteration made to the coin. For example, if one side is weighted, the probability of that side landing face up would be higher than 0.5. If the edges are shaved, the probability of the coin landing on one of those edges would be higher than 0.5. Generally, the probability would be calculated by dividing the number of desired outcomes by the total number of possible outcomes.

Can a rigged coin be used to accurately represent probability?

No, a rigged coin cannot accurately represent probability because its outcome is not based on random chance. Its altered state gives it a predetermined outcome, making it unreliable for representing true probability.

What is the impact of using a rigged coin in scientific research?

Using a rigged coin in scientific research can greatly skew the results and lead to inaccurate conclusions. It goes against the principles of randomness and can introduce bias into the data. Therefore, it is important to use properly weighted and fair coins for any experiments involving probability.

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