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If three coins are tossed at the same time, use a tree diagram to find the probability that exactly one of the coins will land tails up.

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Answer

\( P(exactly \ one \ tails) = P(T_1HT_2T_3) + P(T_1T_2HT_3) + P(HT_1T_2T_3) = \frac{1}{8} + \frac{1}{8} + \frac{1}{8} = \frac{3}{8} \)

Steps

Step 1 ：\( P(T_1HT_2T_3) = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{8} \)

Step 2 ：\( P(T_1T_2HT_3) = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{8} \)

Step 3 ：\( P(HT_1T_2T_3) = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{8} \)

Step 4 ：\( P(exactly \ one \ tails) = P(T_1HT_2T_3) + P(T_1T_2HT_3) + P(HT_1T_2T_3) = \frac{1}{8} + \frac{1}{8} + \frac{1}{8} = \frac{3}{8} \)