document.write( "Question 1182193: A coin is tossed three times, calculate the probability that exactly two of the three tosses results in heads \n" ); document.write( "
Algebra.Com's Answer #812176 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "H = heads
\n" ); document.write( "T = tails\r
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\n" ); document.write( "\n" ); document.write( "There are 2 sides per coin and 3 coins, so we have 2^3 = 8 different ways to flip three coins. This is the same as saying \"there are 8 ways to flip a coin three times\". I think the first interpretation makes more sense (in my opinion).\r
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\n" ); document.write( "\n" ); document.write( "Here are the 8 ways to flip three coins
  1. HHH
  2. HHT
  3. HTH
  4. THH
  5. TTH
  6. THT
  7. HTT
  8. TTT
The stuff highlighted in blue represents getting exactly 2 heads. This happens 3 times. Basically because we have 3 slots, where each tail could go. So the question \"how many ways are there to get 2 heads\" is the same as \"how many ways are there to get 1 tail\".\r
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\n" ); document.write( "\n" ); document.write( "So that's why we end up with the final answer 3/8 (there are 3 ways to get what we want, shown in blue, out of 8 ways total).\r
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\n" ); document.write( "\n" ); document.write( "Here's a more formulaic approach:
\n" ); document.write( "n = 3
\n" ); document.write( "k = 2
\n" ); document.write( "p = 1/2\r
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\n" ); document.write( "\n" ); document.write( "Binomial formula
\n" ); document.write( "P(k) = (n C k)*(p)^k*(1-p)^(n-k)
\n" ); document.write( "P(2) = (3 C 2)*(1/2)^2*(1-1/2)^(3-2)
\n" ); document.write( "P(2) = 3*(1/2)^2*(1/2)^(1)
\n" ); document.write( "P(2) = 3*(1/2)^3
\n" ); document.write( "P(2) = 3*(1/8)
\n" ); document.write( "P(2) = 3/8\r
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\n" ); document.write( "\n" ); document.write( "The n = 3 is the sample size, which is the number of coins we're flipping (or number of coin tosses).
\n" ); document.write( "k = 2 represents the exact number of heads that we want
\n" ); document.write( "p = 1/2 is the probability of flipping heads on any coin
\n" ); document.write( "the notation n C k refers to the combination formula, and it's the exact same number of blue items we counted in the last section. \r
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\n" ); document.write( "\n" ); document.write( "Answer: 3/8
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