hi...this question is from a sample midterm that we went over in class today. i still don't understand certain things. i'm hoping someone can explain it to me.(adsbygoogle = window.adsbygoogle || []).push({});

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consider three identical-looking coins. Two of the coins are ordinary fair coins (H and T are equally likely to occur on any toss), but the third coin is 2-headed (both sides of the coin show H). Fran and Ron each choose a coin at random, and the remaining coin is discarded. Suppose that Fran and Ron toss their coins simultaneously.

Find the probability that Fran gets H and Ron gets H.

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the answer is (1/3)*(1/2)*(1/2)+(2/3)*(1)*(1/2)

the explanation is...you have 1/3 chance of getting a fair coin (heads and tails)

once you get a fair coin, the possibility of getting heads on the first coin is 1/2

and the possibility of getting heads on the second coin is also 1/2

plus

you have 2/3 chance of getting an UNfair coin (heads and heads)

once you get an UNfair coin, the possibility of getting heads on one coin is 1

and the possibility of getting heads on the second coin is also 1/2

could someone please explain why the possibility of choosing the UNfair coin is 2/3 and not 1/3?

you have 2 fair coins so i think that you have double the chances of getting a fair coin than an UNfair coin.

to me it would make perfect sense if the 1/3 and the 2/3 are switched.

thanks,

mark

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# Probability confusion

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