"Construct a sample space to show that the truth of this statment P(A[itex]\bigcap[/itex]B[itex]\bigcap[/itex]C)=P(A)*P(B)*P(C) is not enough for the events A,B,C to be mutually independent.(adsbygoogle = window.adsbygoogle || []).push({});

Hint: Try finite sample spaces with equally likely simple events."

So, my though is that I need to find a sample space with 3 events A, B, C, that are not independent, yet P(A[itex]\bigcap[/itex]B[itex]\bigcap[/itex]C)=P(A)*P(B)*P(C) is true for them.

But I have already tried a couple of simple things and I can't seem to find a proper one. My problem propably lies in the events I take, not the spaces. I tried to use 2 tosses of fair, 6 sided dice, but my events were independent, 10 cards with the numbers 1-10 on them, 2 draws, and the card does not return to the deck. That one had dependent events, but the above statment was not true, and lastly, 2 coin tosses, but again, dependent events, untrue statment.

Any ideas?

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# Find a counterexample for a false statment about independent events.

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