anonymous
  • anonymous
3 fair coins are tossed. What's the probability of obtaining at most 2 heads?
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
1/8
anonymous
  • anonymous
how did you get that?
jim_thompson5910
  • jim_thompson5910
There are 8 possible ways to toss 3 coins and they are HHH HHT HTH HTT THH THT TTH TTT Of this list, there are 7 ways to get either 1 head or 2 heads So the probability is 7/8

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anonymous
  • anonymous
because when you are doing probability, you need to multiply the chance that it will be heads, which is 1 out of 2 or 1/2. therefore it is 1/2 *1/2 which is 1/4 times 1/2 which is 1/8. this is the probability that all of the answers are heads
jim_thompson5910
  • jim_thompson5910
Alternatively, you can compute the probability of getting all tails, which is (1/2)*(1/2)*(1/2) = 1/8 Then subtracting that from 1 to get 1 - 1/8 = 7/8 getting the same answer
anonymous
  • anonymous
but isn't that just exactly 2 heads and not at most 2 heads?
jim_thompson5910
  • jim_thompson5910
oh wait, the probability is still the same, I just mixed up HHH and TTT
anonymous
  • anonymous
@Jim In the list of possibilities, you have HHH counted as one of the "either 1 or 2". Does that mean that the probability is 6/8?
jim_thompson5910
  • jim_thompson5910
I mixed up HHH and TTT on accident I meant to write... There are 8 possible ways to toss 3 coins and they are HHH HHT HTH HTT THH THT TTH TTT Of this list, there are 7 ways to get 0 heads, 1 head or 2 heads (ie "at most 2 heads") Basically, it's everything but HHH. So the probability is 7/8
jim_thompson5910
  • jim_thompson5910
So you can see that the probability is still the same.
anonymous
  • anonymous
oh. TTT is still at most 2 heads. Thank you.
jim_thompson5910
  • jim_thompson5910
Yes as 0 heads is less than that upper max limit.
anonymous
  • anonymous
my bad! i thought that it said all heads! my bad! therefore , the probability is 7/8

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