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16 Sep 2014, 00:26
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If a fair coin, marked with 1 and 2, and a fair six-sided die are rolled together, what is the probability that the sum of their outcomes is even?
A. \(\frac{1}{8}\)
B. \(\frac{1}{4}\)
C. \(\frac{1}{2}\)
D. \(\frac{3}{4}\)
E. \(\frac{7}{8}\)
A. \(\frac{1}{8}\)
B. \(\frac{1}{4}\)
C. \(\frac{1}{2}\)
D. \(\frac{3}{4}\)
E. \(\frac{7}{8}\)
16 Sep 2014, 00:26
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Official Solution:
If a fair coin, marked with 1 and 2, and a fair six-sided die are rolled together, what is the probability that the sum of their outcomes is even?
A. \(\frac{1}{8}\)
B. \(\frac{1}{4}\)
C. \(\frac{1}{2}\)
D. \(\frac{3}{4}\)
E. \(\frac{7}{8}\)
For the sum to be even, the outcomes should either both be odd (odd + odd) or both be even (even + even). Considering this, there are two cases:
• Coin shows 1 (odd) and the die shows 1, 3, or 5 (all odd). The combined probability for this scenario is \(\frac{1}{2} * \frac{3}{6} = \frac{1}{4}\).
• Coin shows 2 (even) and the die shows 2, 4, or 6 (all even). The combined probability of this scenario is \(\frac{1}{2} * \frac{3}{6} = \frac{1}{4}\).
Adding the probabilities from both cases, we get: \( \frac{1}{4}+ \frac{1}{4}= \frac{1}{2}\).
Answer: C
If a fair coin, marked with 1 and 2, and a fair six-sided die are rolled together, what is the probability that the sum of their outcomes is even?
A. \(\frac{1}{8}\)
B. \(\frac{1}{4}\)
C. \(\frac{1}{2}\)
D. \(\frac{3}{4}\)
E. \(\frac{7}{8}\)
For the sum to be even, the outcomes should either both be odd (odd + odd) or both be even (even + even). Considering this, there are two cases:
• Coin shows 1 (odd) and the die shows 1, 3, or 5 (all odd). The combined probability for this scenario is \(\frac{1}{2} * \frac{3}{6} = \frac{1}{4}\).
• Coin shows 2 (even) and the die shows 2, 4, or 6 (all even). The combined probability of this scenario is \(\frac{1}{2} * \frac{3}{6} = \frac{1}{4}\).
Adding the probabilities from both cases, we get: \( \frac{1}{4}+ \frac{1}{4}= \frac{1}{2}\).
Answer: C
18 Oct 2023, 05:59
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
