Question

5. Grayson a green number cube and a white number cube. the faces of the cubes are number 1 through 6. Graysen roll each cube one time. What is the probability that the green cube will land with an even number face up and the white cube will land with a number greater than 2 face up?
A.1/9
B.1/36
C.1/3
D.1/6

Answer 1

Answer: P(G even and W>2) = 1/3 or 0.333 or 33.3%

Step-by-step explanation:

Independent events multiply probabilities,

P(G even)=1/2, P(W>2)=2/3, P(G even and W>2)= 1/2 × 2/3 = 1/3.

Without using definition of "independent events", or rules referring to them, I use sample space S of 36 points, and P(event) = #(event)/#(sample space).

Points are labeled with two digits, left is green die, right is white die. S = {11,12,13,14,15,16,21,...26,...,61,...,66}, and #(S)=36.

An event E is a subset of S, and

0 <= #(E) <= #(S) = 36.

Event G even is GE={21,22,23...,41,42,...,61,...,66},

#(G even)=18

Event "W>2" = W2 ={13,14,15,16,23,24...,63,64,65,66},

#(W>2)=24.

Event G even and W>2 GEW2={23,24,25,26,43,44,45,46,63,64,65,66),

#(GEW2)=12

P(GEW2)=#(GEW2)/#(S)=12/36=1/3=33.3%