Question

select the correct answer.
which sequence of coin flips (h for heads and t for tails) is the most consistent with an unbiased coin?
flip 1 2 3 4 5 6 7 8 9 10 11 12
result h t t t h t t t t h t t
flip 1 2 3 4 5 6 7 8 9 10 11 12
result h h t t t t h t h t t t
flip 1 2 3 4 5 6 7 8 9 10 11 12
result h h h t t h t t h h h h
flip 1 2 3 4 5 6 7 8 9 10 11 12
result t h t h t t t h t t h h

Explanation:

Step1: Calculate the number of heads and tails for each option

• First option:
• Heads (\(H\)): \(3\)
• Tails (\(T\)): \(9\)
• Second option:
• Heads (\(H\)): \(4\)
• Tails (\(T\)): \(8\)
• Third option:
• Heads (\(H\)): \(7\)
• Tails (\(T\)): \(5\)
• Fourth option:
• Heads (\(H\)): \(6\)
• Tails (\(T\)): \(6\)

Step2: Analyze based on the property of an unbiased coin

For an unbiased coin, the probability of getting heads \(P(H)=\frac{1}{2}\) and the probability of getting tails \(P(T)=\frac{1}{2}\). In a sample of \(n = 12\) flips, we expect \(n\times P(H)=12\times\frac{1}{2}=6\) heads and \(n\times P(T) = 12\times\frac{1}{2}=6\) tails.

Answer:

The fourth sequence (where there are 6 heads and 6 tails) is the most consistent with an unbiased coin.