SOLUTION: A coin is tossed three times, calculate the probability that exactly two of the three tosses results in heads
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Question 1182193: A coin is tossed three times, calculate the probability that exactly two of the three tosses results in heads Found 2 solutions by math_tutor2020, ikleyn:Answer by math_tutor2020(3817) (Show Source):
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).
Here are the 8 ways to flip three coins
HHH
HHT
HTH
THH
TTH
THT
HTT
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".
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).
Here's a more formulaic approach:
n = 3
k = 2
p = 1/2
Binomial formula
P(k) = (n C k)*(p)^k*(1-p)^(n-k)
P(2) = (3 C 2)*(1/2)^2*(1-1/2)^(3-2)
P(2) = 3*(1/2)^2*(1/2)^(1)
P(2) = 3*(1/2)^3
P(2) = 3*(1/8)
P(2) = 3/8
The n = 3 is the sample size, which is the number of coins we're flipping (or number of coin tosses).
k = 2 represents the exact number of heads that we want
p = 1/2 is the probability of flipping heads on any coin
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.
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