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To find the probability of getting an even number (2, 4, or 6) between 2 and 4 times when rolling a fair die 8 times, we need to calculate the probabilities of getting 2, 3, or 4 even numbers and add them up.

The probability of getting exactly 2 even numbers is C(8, 2) * (1/2)^2 * (1/2)^6 = 28/256. The probability of getting exactly 3 even numbers is C(8, 3) * (1/2)^3 * (1/2)^5 = 56/256. The probability of getting exactly 4 even numbers is C(8, 4) * (1/2)^4 * (1/2)^4 = 70/256.

Adding these probabilities together, the probability of getting an even number between 2 and 4 times is (28 + 56 + 70)/256 = 154/256 = 77/128.

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Q: If a fair die is rolled 8 times what is the probability that an even number 2 4 6 will occur between 2 and 4 times?
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