molli rolls a 6 sided fair die. find the following probabilities.\np(x is 6):\np(x is larger than 4):\np(x…

Explanation:

Step1: Recall probability formula

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. For a 6 - sided die, the total number of outcomes is $n = 6$.

Step2: Calculate $P(X = 6)$

The number of favorable outcomes for $X = 6$ is 1. So $P(X = 6)=\frac{1}{6}$.

Step3: Calculate $P(X>4)$

The values of $X$ that are greater than 4 are 5 and 6. The number of favorable outcomes is 2. So $P(X>4)=\frac{2}{6}=\frac{1}{3}$.

Step4: Calculate $P(X\geq4)$

The values of $X$ that are at least 4 are 4, 5, and 6. The number of favorable outcomes is 3. So $P(X\geq4)=\frac{3}{6}=\frac{1}{2}$.

Step5: Calculate $P(X\leq4)$

The values of $X$ that are at most 4 are 1, 2, 3, and 4. The number of favorable outcomes is 4. So $P(X\leq4)=\frac{4}{6}=\frac{2}{3}$.

Answer:

$P(X = 6):\frac{1}{6}$ $P(X>4):\frac{1}{3}$ $P(X\geq4):\frac{1}{2}$ $P(X\leq4):\frac{2}{3}$