A fair dice is rolled 5 times. Let $$ x $$ represents the number of times the face 3 turns of obtain probability distribution of $$ x $$.

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Tucker Harris · Accepted Answer

The number of times a **3** appears when rolling a fair die 5 times follows a binomial distribution with parameters $$ n = 5 $$ and $$ p = \frac{1}{6} $$. The probability distribution is: - $$ P(X = 0) \approx 0.4019 $$ - $$ P(X = 1) \approx 0.4019 $$ - $$ P(X = 2) \approx 0.1608 $$ - $$ P(X = 3) \approx 0.0322 $$ - $$ P(X = 4) \approx 0.0032 $$ - $$ P(X = 5) \approx 0.0001 $$ This means: - It's most likely to roll **0** or **1** **3**s. - The probability decreases as the number of **3**s increases. - The distribution is symmetric around lower values due to the low probability of rolling a **3**.

A fair dice is rolled 5 times. Let \( x \) represents the number of times the face 3 turns of obtain probability distribution of \( x \).

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A fair dice is rolled 5 times. Let \( x \) represents the number of times the face 3 turns of obtain probability distribution of \( x \).

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