Math question

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Discus: SAT/ACT Tests and Test Preparation: June 2003 Archive: Math question
 By Confetti (Confetti) on Thursday, June 12, 2003 - 09:48 pm: Edit

A coin is tossed three times. What is the probability that the coin will land on heads at least twice?

I thought the answer would be 1/8, but it turns out to be 1/2. Probability questions kill me. Explanations, anyone? (from act)

 By Andrew123s (Andrew123s) on Thursday, June 12, 2003 - 09:53 pm: Edit

The number of total different outcome combos for the three coints would be 2^3 = 8. Out of these 8 combos, there are 4 possible ones that have 2 or 3 heads:

HHT
HTH
THH
HHH

So out of 8 combos of outcomes, 4 result in at least 2 heads. So the answer is 4/8 or 1/2.

 By Wizzz (Wizzz) on Thursday, June 12, 2003 - 11:44 pm: Edit

Theres a more formulaic approach you can use for that problem too (or any problem with probability). You do the chance of:
exactly 2 heads + the chance of exactly 3 heads

this would be 3C2(.5^2)(.5)+3C3(.5^3)(.5^0)
and this reduces to .375 + .125 which is .5
where C is combinations (you can just use the C key in the calculator if you got a TI-83 or 89)

Say you toss 300 coins and you want to know the chance of say exactly 127 of them landing heads, you would do:
300C127(.5^127)(.5^173) which is .00135. You learn this kind of stuff in pre-calculus

 By Doofus (Doofus) on Friday, June 13, 2003 - 12:33 am: Edit

Hey thanks for the lesson.. I've completed pre-calculus and havent done any of what you described