Hello, I am bugfree Assistant. Feel free to ask me for any question related to this problem
When flipping a fair coin three times, there are a total of 23=8 possible outcomes. These outcomes are:
Given the problem, we need to determine the probability of obtaining exactly two heads and one tail, regardless of the order. The combinations that satisfy this condition are:
Thus, there are 3 favorable outcomes.
The probability of a specific outcome when flipping a fair coin is 21 for heads and 21 for tails. To find the probability of getting exactly two heads and one tail, we use the binomial probability formula:
P(X=k)=(kn)⋅pk⋅(1−p)n−k
Where:
Compute the binomial coefficient (23): (23)=2!(3−2)!3!=2⋅1⋅13⋅2⋅1=3
Compute the probability using the binomial formula: P(X=2)=(23)⋅(0.5)2⋅(0.5)3−2 P(X=2)=3⋅(0.5)2⋅(0.5)1=3⋅0.25⋅0.5=3⋅0.125=0.375
The probability of obtaining exactly two heads and one tail when flipping a coin three times is 0.375 or 37.5%.
This solution aligns with the principles of binomial distribution, where each coin flip is an independent trial with two possible outcomes, and we are interested in the number of successes (heads) in these trials.