MAth Problem ??? Probability??? Help me, please ???

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
daivinhtran
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Joined: Mon Mar 28, 2011 11:43 pm
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MAth Problem ??? Probability??? Help me, please ???

1/ 2 heads or 2 tails appearing in 2 tosses of a coin.
2/ 3 heads or 2 tails appearing in 3 tosses of a coin.
3/ at least 2 heads appearing in 3 tosses of a coin.
4/ at least 3 heads appearing in 4 tosses of a coin.

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And the probabability of obtaining 3 heads in 3 tosses of a coin??????? I tried it by myselfL
BUt I was so confused it.!! If I suppose like 1 event, then I have P=3/6 !!! (Because the outcomes is 6)
But if I suppose like 3 events, then I have P=(1/2) x (1/2) x (1/2)= 1/8
Which one is the correct answer??? Help me, please ???

Martingale
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Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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Re: MAth Problem ??? Probability??? Help me, please ???

1/ 2 heads or 2 tails appearing in 2 tosses of a coin.
2/ 3 heads or 2 tails appearing in 3 tosses of a coin.
3/ at least 2 heads appearing in 3 tosses of a coin.
4/ at least 3 heads appearing in 4 tosses of a coin.

-------------------------------------------------
And the probabability of obtaining 3 heads in 3 tosses of a coin??????? I tried it by myselfL
BUt I was so confused it.!! If I suppose like 1 event, then I have P=3/6 !!! (Because the outcomes is 6)
But if I suppose like 3 events, then I have P=(1/2) x (1/2) x (1/2)= 1/8
Which one is the correct answer??? Help me, please ???
$P(3 Heads)=P(H_1\cap H_2\cap H_3)=P(H_1)P(H_2)P( H_3)=\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{8}$

provided the tosses are independent and the coin is fair.