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Let x represent the difference between t...

Let x represent the difference between the number of heads and the numbers of tails obtained when a coin is tossed 4 times. Then possible values of X is

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To solve the problem, we need to find the possible values of \( x \), which represents the difference between the number of heads and the number of tails when a coin is tossed 4 times. ### Step-by-Step Solution: 1. **Define Variables**: Let \( M \) be the number of heads obtained when the coin is tossed 4 times. Since there are only heads and tails, the number of tails \( N \) can be expressed as \( N = 4 - M \). 2. **Express \( x \)**: The difference \( x \) between the number of heads and the number of tails can be expressed as: \[ x = M - N = M - (4 - M) = 2M - 4 \] 3. **Determine Possible Values of \( M \)**: Since the coin is tossed 4 times, \( M \) can take values from 0 to 4. Therefore, the possible values of \( M \) are: \[ M = 0, 1, 2, 3, 4 \] 4. **Calculate \( x \) for Each Value of \( M \)**: - For \( M = 0 \): \[ x = 2(0) - 4 = -4 \] - For \( M = 1 \): \[ x = 2(1) - 4 = -2 \] - For \( M = 2 \): \[ x = 2(2) - 4 = 0 \] - For \( M = 3 \): \[ x = 2(3) - 4 = 2 \] - For \( M = 4 \): \[ x = 2(4) - 4 = 4 \] 5. **List Possible Values of \( x \)**: The possible values of \( x \) are: \[ -4, -2, 0, 2, 4 \] ### Final Answer: The possible values of \( x \) are \( -4, -2, 0, 2, 4 \).
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