To determine the probability of flipping two tails and two heads in four flips of a coin, we can follow these steps:
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Count the total possible outcomes: Since each coin flip can result in either heads (H) or tails (T), and there are four flips, the total number of outcomes is \( 2^4 = 16 \).
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Count the favorable outcomes: We want to find the number of outcomes that have exactly two heads and two tails. This is a combination problem where we choose 2 flips to be heads (or tails) out of 4. The number of ways to choose 2 heads out of 4 flips is given by: \[ \binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6 \] Therefore, there are 6 favorable outcomes of getting exactly 2 heads and 2 tails.
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Calculate the probability: The probability is given by the ratio of the number of favorable outcomes to the total number of outcomes: \[ P(\text{2 heads, 2 tails}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{6}{16} = \frac{3}{8} \]
Thus, the probability of flipping two tails and two heads in four flips of a coin is \(\frac{3}{8}\).
The answer can be represented as: C. \(\frac{3}{8}\).