Probability, flipping a rigged coin problem

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The discussion revolves around calculating probabilities for a rigged coin with a 52% chance of landing heads and a 48% chance for tails when tossed three times. The probability of getting all heads is calculated as P(all heads) = 0.52 × 0.52 × 0.52 = 0.1406. For the scenario of obtaining 2 tails and 1 head in a specific order, the correct probability is 0.1198, which requires consideration of the order of events. The confusion arises from the need to account for the specific sequence of outcomes, which differs from the independent multiplication used in the all-heads scenario.

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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
 
Physics news on Phys.org
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.
 

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