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If a fair coin is tossed 4 times, what's the probability

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If a fair coin is tossed 4 times, what's the probability [#permalink] New post 25 Nov 2003, 08:48
If a fair coin is tossed 4 times, what's the probability that at least 3 of the 4 tosses will come up heads?

This question is taken directly from a Kaplain guide I have. I know that I can use 2^4 to determine the total possibilities and I can likewise just manually list the number of tosses w/3 heads, but I want to understand the formula. Can someone help me understand this mathematically?

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 [#permalink] New post 26 Nov 2003, 02:41
at least 3 heads means 3 or 4 heads

P(3 heads)=1/2*1/2*1/2*1/2*4C3=4*1/16=4/16
P(4 heads)=1/16

4/16+1/16=5/16
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 [#permalink] New post 26 Nov 2003, 06:34
Alternatively,

You can do the formula for exactly two heads, and divide the "remainder" by two...
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 [#permalink] New post 26 Nov 2003, 08:51
Here's another way of looking at it

No tails HHHH = 4C0 = 1
One Tail THHH = 4C1 = 4
TWO Tails TTHH = 4C2 = 6
Three Tails TTTH = 4C3 = 4
Four Tails TTTT = 4C4 = 1


Total number of desired cases = 5/
Total number of cases = 16

Thus 5/16
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Re: If a fair coin is tossed 4 times, what's the probability [#permalink] New post 24 Sep 2012, 08:30
Expert's post
At least 3 heads from 4 tosses.

# of 3 heads
# of 4 heads

We can use combination to figure out ways that we can pick 3 out of 4 to have heads

4C3

THen add 4C4 - out of 4, choose all four to have heads.

4C3 + 4C4 = total # combinations

2^4 = total # of variations.

Recall that when it comes to coin flipping, it's just one value. Either heads or tails. It's the same idea as in poker, you get one card value but it has 4 variations (hearts, spade, club, or diamond).

In poker, if you got dealt the same card 4 times, you would be looking at 4^4 variations. But with the coin, we only have 2 states (NOT 4 like in poker). So the variations is 2^4

(4C3 + 4C4) / 2^4
= (4 + 1) / 16
= 5/16
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Re: If a fair coin is tossed 4 times, what's the probability   [#permalink] 24 Sep 2012, 08:30
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