Question

initial knowledge check question 8 a weighted number cube has faces labeled 1 through 6. let ( x ) be the number shown on the cube when it is rolled. here is the probability distribution of ( x ).

value ( x ) of ( x )	1	2	3	4	5	6

for parts (a) and (b) below, find the probability that the number described is shown on a random roll.
(a) higher than 4:
(b) less than or equal to 2:

Explanation:

Step1: Identify values higher than 4

Values of $X$ higher than 4 are 5 and 6.

Step2: Sum their probabilities

$P(X>4) = P(X=5) + P(X=6) = 0.12 + 0.11$

Step3: Calculate the total for (a)

$0.12 + 0.11 = 0.23$

Step4: Identify values ≤2

Values of $X$ less than or equal to 2 are 1 and 2.

Step5: Sum their probabilities

$P(X \leq 2) = P(X=1) + P(X=2) = 0.18 + 0.28$

Step6: Calculate the total for (b)

$0.18 + 0.28 = 0.46$

Answer:

(a) $0.23$
(b) $0.46$